zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Spectral radius and Hamiltonian graphs. (English) Zbl 1247.05129
Summary: We present two sufficient conditions for a bipartite graph to be Hamiltonian and a graph to be traceable, respectively.

05C45Eulerian and Hamiltonian graphs
05C50Graphs and linear algebra
15A18Eigenvalues, singular values, and eigenvectors
Full Text: DOI
[1] Berman, A.; Zhang, X. -D.: On the spectral radius of graphs with cut vertices, J. combin. Theory ser. B 83, 233-240 (2001) · Zbl 1023.05098 · doi:10.1006/jctb.2001.2052
[2] Bondy, J. A.; Murty, U. S. R.: Graph theory, Graph theory 244 (2008) · Zbl 1134.05001
[3] Butler, S.; Chung, F.: Small spectral gap in the combinatorial Laplacian implies Hamiltonian, Ann. combin. 13, 403-412 (2010) · Zbl 1229.05193 · doi:10.1007/s00026-009-0039-4
[4] Chvátal, V.: On the Hamilton’s ideal’s, J. combin. Theory ser. B 12, 163-168 (1972) · Zbl 0213.50803 · doi:10.1016/0095-8956(72)90020-2
[5] Fiedler, M.: A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory, Czech math. J. 25, 619-633 (1975) · Zbl 0437.15004
[6] Fiedler, M.; Nikiforov, V.: Spectral radius and hamiltonicity of graphs, Linear algebra appl. 432, 2170-2173 (2010) · Zbl 1218.05091 · doi:10.1016/j.laa.2009.01.005
[7] Haemers, W. H.: Interlacing eigenvalues and graphs, Linear algebra appl. 226 -- 228, 593-616 (1995) · Zbl 0831.05044 · doi:10.1016/0024-3795(95)00199-2
[8] Den Heuvel, J. Van: Hamilton cycles and eigenvalues of graphs, Linear algebra appl. 226 -- 228, 723-730 (1995)
[9] Hofmeister, M.: Spectral radius and degree sequence, Math. nachr. 139, 37-44 (1988) · Zbl 0695.05046 · doi:10.1002/mana.19881390105
[10] Hong, Y.: A bound on the spectral radius of graphs, Linear algebra appl. 108, 135-140 (1988) · Zbl 0655.05047 · doi:10.1016/0024-3795(88)90183-8
[11] Hong, Y.; Shu, J. L.; Fang, K. F.: A sharp upper bound of the spectral radius of graphs, J. combin. Theory ser. B 81, 177-183 (2001) · Zbl 1024.05059 · doi:10.1006/jctb.2000.1997
[12] Horn, R. A.; Johnson, C. R.: Matrix analysis, (1985) · Zbl 0576.15001
[13] Krivelevich, M.; Sudakov, B.: Sparse pseudo-random graphs are Hamiltonian, J. graph theory 42, 17-33 (2003) · Zbl 1028.05059 · doi:10.1002/jgt.10065
[14] Liu, H.; Lu, M.; Tian, F.: On the spectral radius of graphs with cut edges, Linear algebra appl. 389, 139-145 (2004) · Zbl 1053.05080 · doi:10.1016/j.laa.2004.03.026
[15] Mohar, B.: A domain monotonicity theorem for graphs and hamiltonicity, Discrete appl. Math. 36, 169-177 (1992) · Zbl 0765.05071 · doi:10.1016/0166-218X(92)90230-8
[16] Stevanović, D.: The largest eigenvalue of nonregular graphs, J. combin. Theory ser. B 91, 143-146 (2004) · Zbl 1048.05061 · doi:10.1016/j.jctb.2003.12.002
[17] Yu, A.; Lu, M.; Tian, F.: On the spectral radius of graphs, Linear algebra appl. 387, 41-49 (2004) · Zbl 1041.05051 · doi:10.1016/j.laa.2004.01.020