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JGT
2010
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13 years 9 months ago
An approximate version of Hadwiger's conjecture for claw-free graphs
Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class ...
Maria Chudnovsky, Alexandra Ovetsky Fradkin
JCT
2006
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13 years 11 months ago
Every 3-connected, essentially 11-connected line graph is Hamiltonian
Thomassen conjectured that every 4-connected line graph is hamiltonian. A vertex cut X of G is essential if G-X has at least two nontrivial components. We prove that every 3-conne...
Hong-Jian Lai, Yehong Shao, Hehui Wu, Ju Zhou
DM
2006
64views more  DM 2006»
13 years 11 months ago
Path extendability of claw-free graphs
Let G be a connected, locally connected, claw-free graph of order n and x, y be two vertices of G. In this paper, we prove that if for any 2-cut S of G, S {x, y} = , then each (x...
Yu Sheng, Feng Tian, Jianglu Wang, Bing Wei, Yongj...