On hamiltonicity of 2-connected claw-free graphs  被引量:2

On hamiltonicity of 2-connected claw-free graphs

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作  者:TIAN Run-li XIONG Li-ming 

机构地区:[1]Department of Mathematics,Beijing Institute of Technology,Beijing 100081,China [2]Department of Mathematics,Jiangxi Normal University,Nanchang 330022,China

出  处:《Applied Mathematics(A Journal of Chinese Universities)》2012年第2期234-242,共9页高校应用数学学报(英文版)(B辑)

基  金:Supported by the National Natural Science Foundation of China(11071016 and 11171129);the Beijing Natural Science Foundation(1102015)

摘  要:A graph G has the hourglass property if every induced hourglass S(a tree with a degree sequence 22224) contains two non-adjacent vertices which have a common neighbor in G-V(S).For an integer k≥4,a graph G has the single k-cycle property if every edge of G,which does not lie in a triangle,lies in a cycle C of order at most k such that C has at least「|V(C) /2」 edges which do not lie in a triangle,and they are not adjacent.In this paper,we show that every hourglass-free claw-free graph G of δ(G) ≥3 with the single 7-cycle property is Hamiltonian and is best possible;we also show that every claw-free graph G of δ(G) ≥3 with the hourglass property and with single 6-cycle property is Hamiltonian.A graph G has the hourglass property if every induced hourglass S(a tree with a degree sequence 22224) contains two non-adjacent vertices which have a common neighbor in G-V(S).For an integer k≥4,a graph G has the single k-cycle property if every edge of G,which does not lie in a triangle,lies in a cycle C of order at most k such that C has at least「|V(C) /2」 edges which do not lie in a triangle,and they are not adjacent.In this paper,we show that every hourglass-free claw-free graph G of δ(G) ≥3 with the single 7-cycle property is Hamiltonian and is best possible;we also show that every claw-free graph G of δ(G) ≥3 with the hourglass property and with single 6-cycle property is Hamiltonian.

关 键 词:claw-free graph HAMILTONIAN CLOSURE the hourglass property the single k-cycle property. 

分 类 号:O157.5[理学—数学] O11[理学—基础数学]

 

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