计算机科学 ›› 2007, Vol. 34 ›› Issue (8): 227-228.
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摘要: 1988年在美国Kalamazoo召开的"第六届国际图论、组合及其应用会议"上提出无爪图猜想:若3连通n≥3阶K1,3-free图G的不相邻的任两点x、y均有|N(x)∪(N(y)|≥(2n-6)/3,则G是哈密顿图.这里证明更深刻的结果:若3连通n≥3阶K1,3-free图G的满足1≤|N(x)∩(N(y)|≤α-1的不相邻的任两点x、y均有|N(x)∪(N(y)|≥(2n-6)/3,则G是哈密顿图.
关键词: K1,3-free图 邻域并 广义邻域并 哈密顿图
Abstract: In 1998 a conjecture was suggested for the conference of Graph theory, combinatorics, and applications at Kalamazooin USA as follows: let G be a 3-connected K1.3-free graph of order n, if |N(x) ∪N(y) |≥(2n-6)/3 for each pair of nonadjacent vertices x,y, t
Key words: K1,3-free graphs, Neighborhood unions, Generalizing neighborhood unions,Hamiltonian
. 一类K1,3-free Hamiltonian图[J]. 计算机科学, 2007, 34(8): 227-228. https://doi.org/
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