We prove that a 2-connected graph G of order p is traceable if /N(u)boolean OR N(v)/+ /N(w)boolean OR N(x)/greater than or equal to p-1 for all 4-tuples {u, v, w, x} with d(u, v)=d(w, x)=2(u, v, w,x are distinct vertices of G). In addition, we give a short proof of Lindquester's conjecture.
机构:
Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing 100875, Peoples R ChinaBeijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing 100875, Peoples R China
Cai JunLiang
Dong GuangHua
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Tianjin Polytech Univ, Sch Sci, Dept Math, Tianjin 300160, Peoples R ChinaBeijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing 100875, Peoples R China
Dong GuangHua
Liu YanPei
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Beijing Jiaotong Univ, Sch Sci, Dept Math, Beijing 100044, Peoples R ChinaBeijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing 100875, Peoples R China