抄録
Bollobás and Thomason showed that a multigraph of order n and size at least n + c (c ≥ 1) contains a cycle of length at most 2(⌊n/c⌋ + 1) ⌊log2 2c⌋. We show in this paper that a multigraph (with no loop) of order n and minimum degree at least 5 contains a chorded cycle (a cycle with a chord) of length at most 300 log2 n. As an application of this result, we show that a graph of sufficiently large order with minimum degree at least 3k+8 contains k vertex-disjoint chorded cycles of the same length, which is analogous to Verstraëte's result: A graph of sufficiently large order with minimum degree at least 2k contains k vertex-disjoint cycles of the same length.
本文言語 | English |
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ページ(範囲) | 1030-1041 |
ページ数 | 12 |
ジャーナル | SIAM Journal on Discrete Mathematics |
巻 | 29 |
号 | 2 |
DOI | |
出版ステータス | Published - 2015 |
ASJC Scopus subject areas
- 数学 (全般)