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.
| 元の言語 | English |
|---|---|
| ページ（範囲） | 1030-1041 |
| ページ数 | 12 |
| ジャーナル | SIAM Journal on Discrete Mathematics |
| 巻 | 29 |
| 発行部数 | 2 |
| DOI | |
| 出版物ステータス | Published - 2015 |
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ASJC Scopus subject areas
- Mathematics(all)
これを引用
Disjoint chorded cycles of the same length. / Chen, Guantao; Gould, Ronald J.; Hirohata, Kazuhide; Ota, Katsuhiro; Shan, Songling.
：: SIAM Journal on Discrete Mathematics, 巻 29, 番号 2, 2015, p. 1030-1041.研究成果: Article
}
TY - JOUR
T1 - Disjoint chorded cycles of the same length
AU - Chen, Guantao
AU - Gould, Ronald J.
AU - Hirohata, Kazuhide
AU - Ota, Katsuhiro
AU - Shan, Songling
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - Chorded cycles
KW - Cycles
KW - Minimum degree
UR - http://www.scopus.com/inward/record.url?scp=84938094076&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84938094076&partnerID=8YFLogxK
U2 - 10.1137/130929837
DO - 10.1137/130929837
M3 - Article
AN - SCOPUS:84938094076
VL - 29
SP - 1030
EP - 1041
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
SN - 0895-4801
IS - 2
ER -