Hourglasses and Hamilton cycles in 4-connected claw-free graphs
We show that if G is a 4‐connected claw‐free graph in which every induced hourglass subgraph S contains two non‐adjacent vertices with a common neighbor outside S, then G is hamiltonian. This extends the fact that 4‐connected claw‐free, hourglass‐free graphs are hamiltonian, thus proving a broader s...
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| Published in | Journal of graph theory Vol. 48; no. 4; pp. 267 - 276 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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01.04.2005
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| Abstract | We show that if G is a 4‐connected claw‐free graph in which every induced hourglass subgraph S contains two non‐adjacent vertices with a common neighbor outside S, then G is hamiltonian. This extends the fact that 4‐connected claw‐free, hourglass‐free graphs are hamiltonian, thus proving a broader special case of a conjecture by Matthews and Sumner. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 267–276, 2005 |
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| AbstractList | We show that if G is a 4‐connected claw‐free graph in which every induced hourglass subgraph S contains two non‐adjacent vertices with a common neighbor outside S, then G is hamiltonian. This extends the fact that 4‐connected claw‐free, hourglass‐free graphs are hamiltonian, thus proving a broader special case of a conjecture by Matthews and Sumner. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 267–276, 2005 Abstract We show that if G is a 4‐connected claw‐free graph in which every induced hourglass subgraph S contains two non‐adjacent vertices with a common neighbor outside S , then G is hamiltonian. This extends the fact that 4‐connected claw‐free, hourglass‐free graphs are hamiltonian, thus proving a broader special case of a conjecture by Matthews and Sumner. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 267–276, 2005 |
| Author | Xiong, Liming Kaiser, Tomáš Li, MingChu Ryjáček, Zdeněk |
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| Cites_doi | 10.1016/0012-365X(87)90248-2 10.1002/jgt.3190080116 10.1006/jctb.1996.1732 10.1002/jgt.3190160209 10.4153/CMB-1965-051-3 10.1002/jgt.3190120105 10.1016/S0012-365X(98)00334-3 10.1016/0012-365X(91)90302-I 10.1002/jgt.1008 10.1016/0095-8956(74)90087-2 |
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| Notes | Fund of LiuHui Applied Mathematics Research - No. T23 (to M. L.) istex:B66F74F2F08E853FBA62A678AA8EB50A673FA71E Fund of Basic Research of Beijing Institute of Technology (to L. X.) Nature Science Fund of China (to M. L.) ark:/67375/WNG-KMLD358D-D ArticleID:JGT20056 Fund of Natural Science of Jiangxi Province (to L. X.) Czech Ministry of Education - No. ME 418 (to T. K. and Z. R.); No. LN00A056 (to T. K. and Z. R.) |
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| References_xml | – volume: 37 start-page: 125 year: 2001 end-page: 136 article-title: On factors of 4‐connected claw‐free graphs publication-title: J Graph Theory – volume: 70 start-page: 217 issue: 2 year: 1997 end-page: 224 article-title: On a closure concept in claw‐free graphs publication-title: J Comb Theory Ser B – volume: 12 start-page: 29 year: 1988 end-page: 45 article-title: A reduction method to find spanning eulerian subgraphs publication-title: J Graph Theory – volume: 94 start-page: 11 issue: 1 year: 1991 end-page: 22 article-title: Graphs whose edges are in small cycles publication-title: Discrete Math – volume: 8 start-page: 139 year: 1984 end-page: 146 article-title: Hamiltonian results in ‐free graphs publication-title: J Graph Theory – volume: 197/198 start-page: 29 year: 1999 end-page: 50 article-title: Forbidden subgraphs, stability and hamiltonicity publication-title: Discrete Math – volume: 64 start-page: 109 year: 1987 article-title: Research problem publication-title: Discrete Math – volume: 16 start-page: 177 issue: 2 year: 1992 end-page: 196 article-title: Supereulerian graphs: A survey publication-title: J Graph Theory – volume: 8 start-page: 701 year: 1965 end-page: 710 article-title: On eulerian and Hamiltonian graphs and line graphs publication-title: Can Math Bull – volume: 17 start-page: 199 year: 1974 end-page: 203 article-title: Bounds on the number of disjoint spanning trees publication-title: J Combin Theory Ser B – ident: e_1_2_1_10_2 doi: 10.1016/0012-365X(87)90248-2 – ident: e_1_2_1_9_2 doi: 10.1002/jgt.3190080116 – ident: e_1_2_1_11_2 doi: 10.1006/jctb.1996.1732 – ident: e_1_2_1_5_2 doi: 10.1002/jgt.3190160209 – ident: e_1_2_1_6_2 doi: 10.4153/CMB-1965-051-3 – ident: e_1_2_1_4_2 doi: 10.1002/jgt.3190120105 – ident: e_1_2_1_3_2 doi: 10.1016/S0012-365X(98)00334-3 – ident: e_1_2_1_8_2 doi: 10.1016/0012-365X(91)90302-I – ident: e_1_2_1_2_2 doi: 10.1002/jgt.1008 – ident: e_1_2_1_7_2 doi: 10.1016/0095-8956(74)90087-2 |
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| Snippet | We show that if G is a 4‐connected claw‐free graph in which every induced hourglass subgraph S contains two non‐adjacent vertices with a common neighbor... Abstract We show that if G is a 4‐connected claw‐free graph in which every induced hourglass subgraph S contains two non‐adjacent vertices with a common... |
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| SubjectTerms | claw-free graph closure Hamilton cycle hourglass |
| Title | Hourglasses and Hamilton cycles in 4-connected claw-free graphs |
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