Niu, Bei; Zhang, Xin On \((p, 1)\)-total labelling of some 1-planar graphs. (English) Zbl 07308497 Discuss. Math., Graph Theory 41, No. 2, 531-558 (2021). MSC: 05C78 05C10 05C15 PDF BibTeX XML Cite \textit{B. Niu} and \textit{X. Zhang}, Discuss. Math., Graph Theory 41, No. 2, 531--558 (2021; Zbl 07308497) Full Text: DOI
Kindermann, Philipp; Montecchiani, Fabrizio; Schlipf, Lena; Schulz, André Drawing subcubic 1-planar graphs with few bends, few slopes, and large angles. (English) Zbl 1452.05179 J. Graph Algorithms Appl. 25, No. 1, 1-28 (2021). MSC: 05C85 05C10 PDF BibTeX XML Cite \textit{P. Kindermann} et al., J. Graph Algorithms Appl. 25, No. 1, 1--28 (2021; Zbl 1452.05179) Full Text: DOI
Biedl, Therese A note on 1-planar graphs with minimum degree 7. (English) Zbl 07289384 Discrete Appl. Math. 289, 230-232 (2021). MSC: 05C10 05C07 05C35 PDF BibTeX XML Cite \textit{T. Biedl}, Discrete Appl. Math. 289, 230--232 (2021; Zbl 07289384) Full Text: DOI
Bensmail, Julien; Dross, François; Hocquard, Hervé; Sopena, Eric From light edges to strong edge-colouring of 1-planar graphs. (English) Zbl 1452.05053 Discrete Math. Theor. Comput. Sci. 22, No. 1, Paper No. 2, 9 p. (2020). Reviewer: Aleksander Vesel (Maribor) MSC: 05C15 05C10 PDF BibTeX XML Cite \textit{J. Bensmail} et al., Discrete Math. Theor. Comput. Sci. 22, No. 1, Paper No. 2, 9 p. (2020; Zbl 1452.05053) Full Text: DOI
Yang, Wanshun; Wang, Weifan; Wang, Yiqiao An improved upper bound for the acyclic chromatic number of 1-planar graphs. (English) Zbl 1442.05072 Discrete Appl. Math. 283, 275-291 (2020). MSC: 05C15 05C10 PDF BibTeX XML Cite \textit{W. Yang} et al., Discrete Appl. Math. 283, 275--291 (2020; Zbl 1442.05072) Full Text: DOI
Niu, Bei; Zhang, Xin Light edges in 1-planar graphs of minimum degree 3. (English) Zbl 1429.05050 Discrete Math. 343, No. 2, Article ID 111664, 7 p. (2020). MSC: 05C10 05C07 05C35 PDF BibTeX XML Cite \textit{B. Niu} and \textit{X. Zhang}, Discrete Math. 343, No. 2, Article ID 111664, 7 p. (2020; Zbl 1429.05050) Full Text: DOI
Niu, Bei; Zhang, Xin Linear arboricity of NIC-planar graphs. (English) Zbl 1433.05232 Acta Math. Appl. Sin., Engl. Ser. 35, No. 4, 924-934 (2019). MSC: 05C62 05C10 05C07 PDF BibTeX XML Cite \textit{B. Niu} and \textit{X. Zhang}, Acta Math. Appl. Sin., Engl. Ser. 35, No. 4, 924--934 (2019; Zbl 1433.05232) Full Text: DOI
Ouyang, Zhangdong; Ge, Jun; Chen, Yichao Remarks on the joins of 1-planar graphs. (English) Zbl 1433.05089 Appl. Math. Comput. 362, Article ID 124537, 7 p. (2019). MSC: 05C10 05C62 PDF BibTeX XML Cite \textit{Z. Ouyang} et al., Appl. Math. Comput. 362, Article ID 124537, 7 p. (2019; Zbl 1433.05089) Full Text: DOI
Liu, Juan; Hu, Xiaoxue; Wang, Weifan; Wang, Yiqiao Light structures in 1-planar graphs with an application to linear 2-arboricity. (English) Zbl 1419.05056 Discrete Appl. Math. 267, 120-130 (2019). MSC: 05C10 05C70 PDF BibTeX XML Cite \textit{J. Liu} et al., Discrete Appl. Math. 267, 120--130 (2019; Zbl 1419.05056) Full Text: DOI
Zhang, Xin; Niu, Bei; Yu, Jiguo A structure of 1-planar graph and its applications to coloring problems. (English) Zbl 1416.05086 Graphs Comb. 35, No. 3, 677-688 (2019). MSC: 05C10 05C15 05C78 05C62 PDF BibTeX XML Cite \textit{X. Zhang} et al., Graphs Comb. 35, No. 3, 677--688 (2019; Zbl 1416.05086) Full Text: DOI
Brandenburg, Franz J. Characterizing and recognizing 4-map graphs. (English) Zbl 1423.05050 Algorithmica 81, No. 5, 1818-1843 (2019). MSC: 05C10 05C85 68W40 68R10 PDF BibTeX XML Cite \textit{F. J. Brandenburg}, Algorithmica 81, No. 5, 1818--1843 (2019; Zbl 1423.05050) Full Text: DOI
Dvořák, Zdeněk; Venters, Jordan Triangle-free planar graphs with small independence number. (English) Zbl 1402.05044 Eur. J. Comb. 76, 88-103 (2019). MSC: 05C10 05C69 PDF BibTeX XML Cite \textit{Z. Dvořák} and \textit{J. Venters}, Eur. J. Comb. 76, 88--103 (2019; Zbl 1402.05044) Full Text: DOI
Fujisawa, Jun; Segawa, Keita; Suzuki, Yusuke The matching extendability of optimal 1-planar graphs. (English) Zbl 1402.05045 Graphs Comb. 34, No. 5, 1089-1099 (2018). MSC: 05C10 05C70 05C62 PDF BibTeX XML Cite \textit{J. Fujisawa} et al., Graphs Comb. 34, No. 5, 1089--1099 (2018; Zbl 1402.05045) Full Text: DOI
Lu, Zai Ping; Song, Ning Light edges in 3-connected 2-planar graphs with prescribed minimum degree. (English) Zbl 1393.05090 Bull. Malays. Math. Sci. Soc. (2) 41, No. 3, 1265-1274 (2018). MSC: 05C10 05C40 PDF BibTeX XML Cite \textit{Z. P. Lu} and \textit{N. Song}, Bull. Malays. Math. Sci. Soc. (2) 41, No. 3, 1265--1274 (2018; Zbl 1393.05090) Full Text: DOI
Nasiri, Mahboube; Erfanian, Ahmad; Mohammadian, Abbas Connectivity and planarity of \(g\)-noncommuting graph of finite groups. (English) Zbl 1388.05088 J. Algebra Appl. 17, No. 6, Article ID 1850107, 9 p. (2018). MSC: 05C25 05C40 05C10 PDF BibTeX XML Cite \textit{M. Nasiri} et al., J. Algebra Appl. 17, No. 6, Article ID 1850107, 9 p. (2018; Zbl 1388.05088) Full Text: DOI
Zhang, Xin; Wang, Hui-juan; Xu, Lan Equitable coloring of three classes of 1-planar graphs. (English) Zbl 1387.05099 Acta Math. Appl. Sin., Engl. Ser. 34, No. 2, 362-372 (2018). MSC: 05C15 05C10 PDF BibTeX XML Cite \textit{X. Zhang} et al., Acta Math. Appl. Sin., Engl. Ser. 34, No. 2, 362--372 (2018; Zbl 1387.05099) Full Text: DOI
Zhang, Xin; Lan, Jingfen; Li, Bi; Zhu, Qiang Light paths and edges in families of outer-1-planar graphs. (English) Zbl 06873294 Inf. Process. Lett. 136, 83-89 (2018). MSC: 68Q PDF BibTeX XML Cite \textit{X. Zhang} et al., Inf. Process. Lett. 136, 83--89 (2018; Zbl 06873294) Full Text: DOI
Hudák, Peter; Maceková, Mária; Madaras, Tomáš; Široczki, Pavol More on the structure of plane graphs with prescribed degrees of vertices, faces, edges and dual edges. (English) Zbl 1380.05035 Ars Math. Contemp. 13, No. 2, 355-366 (2017). MSC: 05C10 05C07 05C22 05C35 05C75 PDF BibTeX XML Cite \textit{P. Hudák} et al., Ars Math. Contemp. 13, No. 2, 355--366 (2017; Zbl 1380.05035) Full Text: DOI
Bekos, Michael A.; Bruckdorfer, Till; Kaufmann, Michael; Raftopoulou, Chrysanthi N. The book thickness of 1-planar graphs is constant. (English) Zbl 1372.05049 Algorithmica 79, No. 2, 444-465 (2017). MSC: 05C10 05C62 05C85 PDF BibTeX XML Cite \textit{M. A. Bekos} et al., Algorithmica 79, No. 2, 444--465 (2017; Zbl 1372.05049) Full Text: DOI
Bekos, Michael A.; Cornelsen, Sabine; Grilli, Luca; Hong, Seok-Hee; Kaufmann, Michael On the recognition of fan-planar and maximal outer-fan-planar graphs. (English) Zbl 1372.68201 Algorithmica 79, No. 2, 401-427 (2017). MSC: 68R10 05C10 05C85 PDF BibTeX XML Cite \textit{M. A. Bekos} et al., Algorithmica 79, No. 2, 401--427 (2017; Zbl 1372.68201) Full Text: DOI
Kobourov, Stephen G.; Liotta, Giuseppe; Montecchiani, Fabrizio An annotated bibliography on 1-planarity. (English) Zbl 1398.68402 Comput. Sci. Rev. 25, 49-67 (2017). MSC: 68R10 05C10 68-02 PDF BibTeX XML Cite \textit{S. G. Kobourov} et al., Comput. Sci. Rev. 25, 49--67 (2017; Zbl 1398.68402) Full Text: DOI
Suzuki, Yusuke \(K_7\)-minors in optimal 1-planar graphs. (English) Zbl 1369.05188 Discrete Math. 340, No. 6, 1227-1234 (2017). MSC: 05C83 05C10 PDF BibTeX XML Cite \textit{Y. Suzuki}, Discrete Math. 340, No. 6, 1227--1234 (2017; Zbl 1369.05188) Full Text: DOI
Lenhart, William J.; Liotta, Giuseppe; Montecchiani, Fabrizio On partitioning the edges of 1-plane graphs. (English) Zbl 1357.05125 Theor. Comput. Sci. 662, 59-65 (2017). MSC: 05C70 05C10 PDF BibTeX XML Cite \textit{W. J. Lenhart} et al., Theor. Comput. Sci. 662, 59--65 (2017; Zbl 1357.05125) Full Text: DOI
Hong, Seok-Hee; Nagamochi, Hiroshi Re-embedding a 1-plane graph into a straight-line drawing in linear time. (English) Zbl 06687306 Hu, Yifan (ed.) et al., Graph drawing and network visualization. 24th international symposium, GD 2016, Athens, Greece, September 19–21, 2016. Revised selected papers. Cham: Springer (ISBN 978-3-319-50105-5/pbk; 978-3-319-50106-2/ebook). Lecture Notes in Computer Science 9801, 321-334 (2016). MSC: 68R10 68U05 PDF BibTeX XML Cite \textit{S.-H. Hong} and \textit{H. Nagamochi}, Lect. Notes Comput. Sci. 9801, 321--334 (2016; Zbl 06687306) Full Text: DOI
Zhang, Xin On equitable colorings of sparse graphs. (English) Zbl 1339.05150 Bull. Malays. Math. Sci. Soc. (2) 39, Suppl. 1, S257-S268 (2016). MSC: 05C15 05C10 05C07 PDF BibTeX XML Cite \textit{X. Zhang}, Bull. Malays. Math. Sci. Soc. (2) 39, S257--S268 (2016; Zbl 1339.05150) Full Text: DOI
Horňák, Mirko; Jendrol’, Stanislav; Schiermeyer, Ingo On the maximum weight of a sparse connected graph of given order and size. (English) Zbl 1339.05168 Graphs Comb. 32, No. 3, 997-1012 (2016). MSC: 05C22 05C40 PDF BibTeX XML Cite \textit{M. Horňák} et al., Graphs Comb. 32, No. 3, 997--1012 (2016; Zbl 1339.05168) Full Text: DOI
Auer, Christopher; Bachmaier, Christian; Brandenburg, Franz J.; Gleißner, Andreas; Hanauer, Kathrin; Neuwirth, Daniel; Reislhuber, Josef Outer 1-planar graphs. (English) Zbl 1339.68197 Algorithmica 74, No. 4, 1293-1320 (2016). MSC: 68R10 05C10 05C85 PDF BibTeX XML Cite \textit{C. Auer} et al., Algorithmica 74, No. 4, 1293--1320 (2016; Zbl 1339.68197) Full Text: DOI
Horňák, Mirko; Jendrol’, Stanislav; Schiermeyer, Ingo On the maximum weight of a dense connected graph of given order and size. (English) Zbl 1334.05055 Discrete Math. 339, No. 7, 1978-1984 (2016). MSC: 05C22 05C42 05C40 05C35 PDF BibTeX XML Cite \textit{M. Horňák} et al., Discrete Math. 339, No. 7, 1978--1984 (2016; Zbl 1334.05055) Full Text: DOI
Czap, Július; Przybyło, Jakub; Škrabuľáková, Erika On an extremal problem in the class of bipartite 1-planar graphs. (English) Zbl 1329.05081 Discuss. Math., Graph Theory 36, No. 1, 141-151 (2016). MSC: 05C10 05C42 05C62 PDF BibTeX XML Cite \textit{J. Czap} et al., Discuss. Math., Graph Theory 36, No. 1, 141--151 (2016; Zbl 1329.05081) Full Text: DOI
Fabrici, I.; Jendrol’, S.; Vrbjarová, M. Facial entire colouring of plane graphs. (English) Zbl 1327.05108 Discrete Math. 339, No. 2, 626-631 (2016). MSC: 05C15 05C10 PDF BibTeX XML Cite \textit{I. Fabrici} et al., Discrete Math. 339, No. 2, 626--631 (2016; Zbl 1327.05108) Full Text: DOI
Noguchi, Kenta; Suzuki, Yusuke Relationship among triangulations, quadrangulations and optimal 1-planar graphs. (English) Zbl 1329.05088 Graphs Comb. 31, No. 6, 1965-1972 (2015). MSC: 05C10 PDF BibTeX XML Cite \textit{K. Noguchi} and \textit{Y. Suzuki}, Graphs Comb. 31, No. 6, 1965--1972 (2015; Zbl 1329.05088) Full Text: DOI
Hong, Seok-Hee; Eades, Peter; Katoh, Naoki; Liotta, Giuseppe; Schweitzer, Pascal; Suzuki, Yusuke A linear-time algorithm for testing outer-1-planarity. (English) Zbl 1319.68158 Algorithmica 72, No. 4, 1033-1054 (2015). MSC: 68R10 05C10 05C85 PDF BibTeX XML Cite \textit{S.-H. Hong} et al., Algorithmica 72, No. 4, 1033--1054 (2015; Zbl 1319.68158) Full Text: DOI
Czap, Július; Hudák, Dávid; Madaras, Tomáš Joins of 1-planar graphs. (English) Zbl 1304.05024 Acta Math. Sin., Engl. Ser. 30, No. 11, 1867-1876 (2014). MSC: 05C10 05C62 PDF BibTeX XML Cite \textit{J. Czap} et al., Acta Math. Sin., Engl. Ser. 30, No. 11, 1867--1876 (2014; Zbl 1304.05024) Full Text: DOI arXiv
Ackerman, Eyal A note on 1-planar graphs. (English) Zbl 1298.05081 Discrete Appl. Math. 175, 104-108 (2014). MSC: 05C10 05C62 PDF BibTeX XML Cite \textit{E. Ackerman}, Discrete Appl. Math. 175, 104--108 (2014; Zbl 1298.05081) Full Text: DOI
Czap, Július; Harant, Jochen; Hudák, Dávid An upper bound on the sum of powers of the degrees of simple 1-planar graphs. (English) Zbl 1288.05051 Discrete Appl. Math. 165, 146-151 (2014). MSC: 05C10 05C07 PDF BibTeX XML Cite \textit{J. Czap} et al., Discrete Appl. Math. 165, 146--151 (2014; Zbl 1288.05051) Full Text: DOI
Korzhik, Vladimir P. Proper 1-immersions of graphs triangulating the plane. (English) Zbl 1280.05030 Discrete Math. 313, No. 23, 2673-2686 (2013). MSC: 05C10 05C62 PDF BibTeX XML Cite \textit{V. P. Korzhik}, Discrete Math. 313, No. 23, 2673--2686 (2013; Zbl 1280.05030) Full Text: DOI
Xu, Renyu; Wu, Jianliang; Wang, Guanghui; Zhang, Xin On the sum of powers of the degrees of graphs. (English) Zbl 1296.05051 Bull. Aust. Math. Soc. 88, No. 3, 353-358 (2013). Reviewer: Lili Hu (Zhangzhou) MSC: 05C07 05C10 PDF BibTeX XML Cite \textit{R. Xu} et al., Bull. Aust. Math. Soc. 88, No. 3, 353--358 (2013; Zbl 1296.05051) Full Text: DOI
Eades, Peter; Hong, Seok-Hee; Katoh, Naoki; Liotta, Giuseppe; Schweitzer, Pascal; Suzuki, Yusuke A linear time algorithm for testing maximal 1-planarity of graphs with a rotation system. (English) Zbl 1407.68354 Theor. Comput. Sci. 513, 65-76 (2013). MSC: 68R10 05C85 68W40 PDF BibTeX XML Cite \textit{P. Eades} et al., Theor. Comput. Sci. 513, 65--76 (2013; Zbl 1407.68354) Full Text: DOI
Zhang, Xin; Liu, Gui Zhen On edge colorings of 1-toroidal graphs. (English) Zbl 1268.05053 Acta Math. Sin., Engl. Ser. 29, No. 7, 1421-1428 (2013). MSC: 05C10 05C15 05C07 05C35 PDF BibTeX XML Cite \textit{X. Zhang} and \textit{G. Z. Liu}, Acta Math. Sin., Engl. Ser. 29, No. 7, 1421--1428 (2013; Zbl 1268.05053) Full Text: DOI
Eades, Peter; Liotta, Giuseppe Right angle crossing graphs and 1-planarity. (English) Zbl 1408.05042 Discrete Appl. Math. 161, No. 7-8, 961-969 (2013). MSC: 05C10 05C62 05C35 05C76 68R10 PDF BibTeX XML Cite \textit{P. Eades} and \textit{G. Liotta}, Discrete Appl. Math. 161, No. 7--8, 961--969 (2013; Zbl 1408.05042) Full Text: DOI
Korzhik, Vladimir P.; Mohar, Bojan Minimal obstructions for 1-immersions and hardness of 1-planarity testing. (English) Zbl 1259.05046 J. Graph Theory 72, No. 1-2, 30-71 (2013). MSC: 05C10 PDF BibTeX XML Cite \textit{V. P. Korzhik} and \textit{B. Mohar}, J. Graph Theory 72, No. 1--2, 30--71 (2013; Zbl 1259.05046) Full Text: DOI
Zhang, Xin; Liu, Guizhen The structure of plane graphs with independent crossings and its applications to coloring problems. (English) Zbl 1258.05028 Cent. Eur. J. Math. 11, No. 2, 308-321 (2013). MSC: 05C10 05C62 05C15 05C35 PDF BibTeX XML Cite \textit{X. Zhang} and \textit{G. Liu}, Cent. Eur. J. Math. 11, No. 2, 308--321 (2013; Zbl 1258.05028) Full Text: DOI
Zhang, Xin; Wu, Jianliang; Liu, Guizhen List edge and list total coloring of 1-planar graphs. (English) Zbl 1254.05050 Front. Math. China 7, No. 5, 1005-1018 (2012). MSC: 05C10 05C15 05C07 05C35 PDF BibTeX XML Cite \textit{X. Zhang} et al., Front. Math. China 7, No. 5, 1005--1018 (2012; Zbl 1254.05050) Full Text: DOI
Zhang, Xin; Liu, Gui Zhen; Wu, Jian Liang Light subgraphs in the family of 1-planar graphs with high minimum degree. (English) Zbl 1252.05047 Acta Math. Sin., Engl. Ser. 28, No. 6, 1155-1168 (2012). MSC: 05C10 05C75 PDF BibTeX XML Cite \textit{X. Zhang} et al., Acta Math. Sin., Engl. Ser. 28, No. 6, 1155--1168 (2012; Zbl 1252.05047) Full Text: DOI
Zhang, Xin; Liu, Guizhen On edge colorings of 1-planar graphs without adjacent triangles. (English) Zbl 1239.05078 Inf. Process. Lett. 112, No. 4, 138-142 (2012). MSC: 05C15 05C07 05C10 PDF BibTeX XML Cite \textit{X. Zhang} and \textit{G. Liu}, Inf. Process. Lett. 112, No. 4, 138--142 (2012; Zbl 1239.05078) Full Text: DOI
Czap, Július; Hudák, Dávid 1-planarity of complete multipartite graphs. (English) Zbl 1239.05039 Discrete Appl. Math. 160, No. 4-5, 505-512 (2012). MSC: 05C10 05C70 PDF BibTeX XML Cite \textit{J. Czap} and \textit{D. Hudák}, Discrete Appl. Math. 160, No. 4--5, 505--512 (2012; Zbl 1239.05039) Full Text: DOI
Eades, Peter; Liotta, Giuseppe Right angle crossing graphs and 1-planarity. (English) Zbl 1311.68115 van Kreveld, Marc (ed.) et al., Graph drawing. 19th international symposium, GD 2011, Eindhoven, The Netherlands, September 21–23, 2011. Revised selected papers. Berlin: Springer (ISBN 978-3-642-25877-0/pbk). Lecture Notes in Computer Science 7034, 148-153 (2012). MSC: 68R10 05C10 05C62 68U05 PDF BibTeX XML Cite \textit{P. Eades} and \textit{G. Liotta}, Lect. Notes Comput. Sci. 7034, 148--153 (2012; Zbl 1311.68115) Full Text: DOI
Harant, Jochen; Jendrol’, Stanislav Nonrepetitive vertex colorings of graphs. (English) Zbl 1233.05103 Discrete Math. 312, No. 2, 374-380 (2012). MSC: 05C15 05C10 PDF BibTeX XML Cite \textit{J. Harant} and \textit{S. Jendrol'}, Discrete Math. 312, No. 2, 374--380 (2012; Zbl 1233.05103) Full Text: DOI
Zhang, Xin; Wu, Jian-Liang On edge colorings of \(1\)-planar graphs. (English) Zbl 1259.05050 Inf. Process. Lett. 111, No. 3, 124-128 (2011). MSC: 05C10 05C15 05C62 PDF BibTeX XML Cite \textit{X. Zhang} and \textit{J.-L. Wu}, Inf. Process. Lett. 111, No. 3, 124--128 (2011; Zbl 1259.05050) Full Text: DOI
Zhang, Xin; Yu, Yong; Liu, Guizhen On \((p,1)\)-total labelling of 1-planar graphs. (English) Zbl 1227.05135 Cent. Eur. J. Math. 9, No. 6, 1424-1434 (2011). MSC: 05C10 05C15 05C78 PDF BibTeX XML Cite \textit{X. Zhang} et al., Cent. Eur. J. Math. 9, No. 6, 1424--1434 (2011; Zbl 1227.05135) Full Text: DOI
Suzuki, Yusuke Optimal 1-planar graphs which triangulate other surfaces. (English) Zbl 1188.05056 Discrete Math. 310, No. 1, 6-11 (2010). Reviewer: Stelian Mihalas (Timişoara) MSC: 05C10 68R10 PDF BibTeX XML Cite \textit{Y. Suzuki}, Discrete Math. 310, No. 1, 6--11 (2010; Zbl 1188.05056) Full Text: DOI
Korzhik, Vladimir P. Minimal non-1-planar graphs. (English) Zbl 1132.05014 Discrete Math. 308, No. 7, 1319-1327 (2008). MSC: 05C10 PDF BibTeX XML Cite \textit{V. P. Korzhik}, Discrete Math. 308, No. 7, 1319--1327 (2008; Zbl 1132.05014) Full Text: DOI