Degree sums for edges and cycle lengths in graphs

被引:0
|
作者
Brandt, S [1 ]
Veldman, HJ [1 ]
机构
[1] UNIV TWENTE,FAC APPL MATH,NL-7500 AE ENSCHEDE,NETHERLANDS
关键词
degree sum; circumference; cycle hamiltonian graph; pancyclic graph; tough graph; closure;
D O I
10.1002/(SICI)1097-0118(199708)25:4<253::AID-JGT2>3.0.CO;2-J
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let G be a graph of order n, satisfying d(u) + d(v) greater than or equal to n,for every edge uv of G. We show that the circumference - the length of a longest cycle - of G can be expressed in terms of a certain graph parameter, and can be computed in polynomial time. Moreover, we show that G contains cycles of every length between 3 and the circumference, unless G is complete bipartite. If G is 1-tough then it is pancyclic or G = K-r,K-r with r = n/2. (C) 1997 John Wiley & Sons, Inc.
引用
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页码:253 / 256
页数:4
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