机构:
Ctr Math Sci, Dept Pure Math & Math Stat, Cambridge CB3 0WB, EnglandCtr Math Sci, Dept Pure Math & Math Stat, Cambridge CB3 0WB, England
Verstraëte, J
[1
]
机构:
[1] Ctr Math Sci, Dept Pure Math & Math Stat, Cambridge CB3 0WB, England
来源:
COMBINATORICS PROBABILITY & COMPUTING
|
2002年
/
11卷
/
01期
关键词:
D O I:
10.1017/S0963548301004904
中图分类号:
TP301 [理论、方法];
学科分类号:
081202 ;
摘要:
Haggkvist and Scott asked whether one can find a quadratic function q(k) such that, if G is a graph of minimum degree at least q(k), then G contains vertex-disjoint cycles of k consecutive even lengths. In this paper, it is shown that if G is a graph of average degree at least k(2) + 19k + 10 with sufficiently many vertices, then G contains vertex-disjoint cycles of k consecutive even lengths, answering the above question in the affirmative. The coefficient of k(2) cannot be decreased and, in this sense, this result is best possible.