Bérczi, Kristóf; Hoang, Hung P.; Tóthmérész, Lilla On approximating the rank of graph divisors. (English) Zbl 1516.05141 Discrete Math. 346, No. 9, Article ID 113528, 8 p. (2023). MSC: 05C57 91A43 05C70 14H55 68Q25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bu, Alan; Choi, Yunseo; Xu, Max An exact bound on the number of chips of parallel chip-firing games that stabilize. (English) Zbl 1500.05042 Arch. Math. 119, No. 5, 471-478 (2022). MSC: 05C57 05C85 68R10 37B15 68Q25 68W05 91A43 × Cite Format Result Cite Review PDF Full Text: DOI
Aidun, Ivan; Dean, Frances; Morrison, Ralph; Yu, Teresa; Yuan, Julie Gonality sequences of graphs. (English) Zbl 1460.14142 SIAM J. Discrete Math. 35, No. 2, 814-839 (2021). MSC: 14T15 14H51 05C25 05C57 05C85 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gao, Yibo; Li, Rupert Compatible recurrent identities of the sandpile group and maximal stable configurations. (English) Zbl 1451.05172 Discrete Appl. Math. 288, 123-137 (2021). MSC: 05C69 05C35 05C76 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bodewes, Jelco M.; Bodlaender, Hans L.; Cornelissen, Gunther; van der Wegen, Marieke Recognizing hyperelliptic graphs in polynomial time. (English) Zbl 1436.05105 Theor. Comput. Sci. 815, 121-146 (2020). MSC: 05C85 05C10 × Cite Format Result Cite Review PDF Full Text: DOI
Holroyd, Alexander E.; Levine, Lionel; Winkler, Peter Abelian logic gates. (English) Zbl 1433.68138 Comb. Probab. Comput. 28, No. 3, 388-422 (2019). MSC: 68Q06 68Q10 68Q45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nguyen, Viet-Ha; Perrot, Kévin Any shape can ultimately cross information on two-dimensional abelian sandpile models. (English) Zbl 1515.37013 Baetens, Jan M. (ed.) et al., Cellular automata and discrete complex systems. 24th IFIP WG 1.5 international workshop, AUTOMATA 2018, Ghent, Belgium, June 20–22, 2018. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10875, 127-142 (2018). MSC: 37B15 37B10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Bodewes, Jelco M.; Bodlaender, Hans L.; Cornelissen, Gunther; van der Wegen, Marieke Recognizing hyperelliptic graphs in polynomial time. (English) Zbl 1517.68276 Brandstädt, Andreas (ed.) et al., Graph-theoretic concepts in computer science. 44th international workshop, WG 2018, Cottbus, Germany, June 27–29, 2018. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11159, 52-64 (2018). MSC: 68R10 05C85 68Q25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Cairns, Hannah Some halting problems for abelian sandpiles are undecidable in dimension three. (English) Zbl 1403.68133 SIAM J. Discrete Math. 32, No. 4, 2636-2666 (2018). MSC: 68Q80 68Q05 68Q10 68Q17 91A43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chan, Swee Hong Abelian sandpile model and Biggs-Merino polynomial for directed graphs. (English) Zbl 1373.05075 J. Comb. Theory, Ser. A 154, 145-171 (2018). MSC: 05C20 05C31 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Farrell, Matthew; Levine, Lionel CoEulerian graphs. (English) Zbl 1334.05025 Proc. Am. Math. Soc. 144, No. 7, 2847-2860 (2016). MSC: 05C05 05C20 05C45 05C50 68Q25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bond, Benjamin; Levine, Lionel Abelian networks. II: Halting on all inputs. (English) Zbl 1369.68208 Sel. Math., New Ser. 22, No. 1, 319-340 (2016). Reviewer: Damas Gruska (Bratislava) MSC: 68Q10 05C50 37B15 20M14 20M35 68Q05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhuang, Wei; Yang, Weihua; Zhang, Lianzhu; Guo, Xiaofeng Properties of chip-firing games on complete graphs. (English) Zbl 1322.05096 Bull. Malays. Math. Sci. Soc. (2) 38, No. 4, 1463-1469 (2015). MSC: 05C57 91A43 × Cite Format Result Cite Review PDF Full Text: DOI
Choure, Ayush; Vishwanathan, Sundar On graph parameters guaranteeing fast sandpile diffusion. (English) Zbl 1308.05097 Electron. J. Comb. 22, No. 1, Research Paper P1.44, 32 p. (2015). MSC: 05C81 05C25 05C90 82C20 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Choure, Ayush; Vishwanathan, Sundar Random walks, electric networks and the transience class problem of sandpiles. (English) Zbl 1423.05157 Rabani, Yuval (ed.), Proceedings of the 23rd annual ACM-SIAM symposium on discrete algorithms, SODA 2012, Kyoto, Japan, January 17–19, 2012. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM); New York, NY: Association for Computing Machinery (ACM). 1593-1611 (2012). MSC: 05C81 05C50 82C20 94C15 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Mejia, Carolina; Montoya, J. Andres On the complexity of sandpile critical avalanches. (English) Zbl 1216.68132 Theor. Comput. Sci. 412, No. 30, 3964-3974 (2011). MSC: 68Q25 68Q17 68Q80 37B15 × Cite Format Result Cite Review PDF Full Text: DOI
Kominers, Paul Myer; Kominers, Scott Duke A constant bound for the periods of parallel chip-firing games with many chips. (English) Zbl 1230.05212 Arch. Math. 95, No. 1, 9-13 (2010). MSC: 05C57 05C35 05C85 68Q25 37B15 68R10 68Q80 × Cite Format Result Cite Review PDF Full Text: DOI
Mejía, Carolina; Andrés Montoya, J. The complexity of three-dimensional critical avalanches. (English) Zbl 1306.68045 Bandini, Stefania (ed.) et al., Cellular automata. 9th international conference on cellular automata for research and industry, ACRI 2010, Ascoli Piceno, Italy, September 21–24, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-15978-7/pbk). Lecture Notes in Computer Science 6350, 153-162 (2010). MSC: 68Q25 68Q80 76T25 × Cite Format Result Cite Review PDF Full Text: DOI
Montoya, J. Andrés; Mejía, Carolina On the complexity of sandpile prediction problems. (English) Zbl 1338.68188 de Oliveira, Pedro P. B. (ed.) et al., Proceedings of the 15th international workshop on cellular automata and discrete complex systems, São Paulo, Brazil, October 10–12, 2009. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 252, 229-245 (2009). MSC: 68Q80 68Q15 × Cite Format Result Cite Review PDF Full Text: DOI
Baker, Matthew; Norine, Serguei Riemann-Roch and Abel-Jacobi theory on a finite graph. (English) Zbl 1124.05049 Adv. Math. 215, No. 2, 766-788 (2007). MSC: 05C38 14H55 05C25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Toumpakari, Evelin On the sandpile group of regular trees. (English) Zbl 1120.05042 Eur. J. Comb. 28, No. 3, 822-842 (2007). Reviewer: Robert Jajcay (Terre Haute) MSC: 05C25 05C05 05E99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Merino, Criel The chip-firing game. (English) Zbl 1139.91314 Discrete Math. 302, No. 1-3, 188-210 (2005). MSC: 91A43 05C90 05B35 × Cite Format Result Cite Review PDF Full Text: DOI
Goles, Eric; Prisner, Erich Source reversal and chip firing on graphs. (English) Zbl 0947.05039 Theor. Comput. Sci. 233, No. 1-2, 287-295 (2000). Reviewer: Josep M.Brunat Blay (Barcelona) MSC: 05C20 68R10 × Cite Format Result Cite Review PDF Full Text: DOI
Goles, Eric; Margenstern, Maurice Universality of the chip-firing game. (English) Zbl 0903.68138 Theor. Comput. Sci. 172, No. 1-2, 121-134 (1997). MSC: 68R10 91A46 × Cite Format Result Cite Review PDF Full Text: DOI
Jeffs, Janice; Seager, Suzanne The chip firing game on \(n\)-cycles. (English) Zbl 0833.90148 Graphs Comb. 11, No. 1, 59-67 (1995). MSC: 91A43 05C99 05C38 × Cite Format Result Cite Review PDF Full Text: DOI
Kiwi, M. A.; Ndoundam, R.; Tchuente, M.; Goles, E. No polynomial bound for the period of the parallel chip firing game on graphs. (English) Zbl 0874.68229 Theor. Comput. Sci. 136, No. 2, 527-532 (1994). MSC: 68R10 68M07 × Cite Format Result Cite Review PDF Full Text: DOI
Björner, Anders; Lovász, László Chip-firing games on directed graphs. (English) Zbl 0805.90142 J. Algebr. Comb. 1, No. 4, 305-328 (1992). MSC: 91A43 60G50 05C20 × Cite Format Result Cite Review PDF Full Text: DOI
Bitar, Javier; Goles, Eric Parallel chip firing games on graphs. (English) Zbl 0745.05054 Theor. Comput. Sci. 92, No. 2, 291-300 (1992). Reviewer: Liu Zhenhong (Beijing) MSC: 05C99 68R10 × Cite Format Result Cite Review PDF Full Text: DOI
Goles, Eric Sand pile automata. (English) Zbl 0791.68118 Ann. Inst. Henri Poincaré, Phys. Théor. 56, No. 1, 75-90 (1992). MSC: 68Q80 37B99 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML
Björner, Anders; Lovász, László; Shor, Peter W. Chip-firing games on graphs. (English) Zbl 0729.05048 Eur. J. Comb. 12, No. 4, 283-291 (1991). MSC: 05C99 90C10 × Cite Format Result Cite Review PDF Full Text: DOI
Eriksson, Kimmo No polynomial bound for the chip firing game on directed graphs. (English) Zbl 0758.05060 Proc. Am. Math. Soc. 112, No. 4, 1203-1205 (1991). MSC: 05C35 05C20 × Cite Format Result Cite Review PDF Full Text: DOI