A degree sum condition for long cycles passing through a linear forest

Jun Fujisawa, Tomoki Yamashita

Research output: Contribution to journalArticle

Abstract

Let G be a (k + m)-connected graph and F be a linear forest in G such that | E (F) | = m and F has at most k - 2 components of order 1, where k ≥ 2 and m ≥ 0. In this paper, we prove that if every independent set S of G with | S | = k + 1 contains two vertices whose degree sum is at least d, then G has a cycle C of length at least min { d - m, | V (G) | } which contains all the vertices and edges of F.

Original languageEnglish
Pages (from-to)2382-2388
Number of pages7
JournalDiscrete Mathematics
Volume308
Issue number12
DOIs
Publication statusPublished - 2008 Jun 28
Externally publishedYes

Fingerprint

Degree Sum
Long Cycle
Vertex Degree
Independent Set
Connected graph
Cycle

Keywords

  • Degree sum
  • Linear forest
  • Long cycle

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

A degree sum condition for long cycles passing through a linear forest. / Fujisawa, Jun; Yamashita, Tomoki.

In: Discrete Mathematics, Vol. 308, No. 12, 28.06.2008, p. 2382-2388.

Research output: Contribution to journalArticle

Fujisawa, Jun ; Yamashita, Tomoki. / A degree sum condition for long cycles passing through a linear forest. In: Discrete Mathematics. 2008 ; Vol. 308, No. 12. pp. 2382-2388.
@article{a23710ebfe6241479fa4b0f126952659,
title = "A degree sum condition for long cycles passing through a linear forest",
abstract = "Let G be a (k + m)-connected graph and F be a linear forest in G such that | E (F) | = m and F has at most k - 2 components of order 1, where k ≥ 2 and m ≥ 0. In this paper, we prove that if every independent set S of G with | S | = k + 1 contains two vertices whose degree sum is at least d, then G has a cycle C of length at least min { d - m, | V (G) | } which contains all the vertices and edges of F.",
keywords = "Degree sum, Linear forest, Long cycle",
author = "Jun Fujisawa and Tomoki Yamashita",
year = "2008",
month = "6",
day = "28",
doi = "10.1016/j.disc.2007.05.005",
language = "English",
volume = "308",
pages = "2382--2388",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "12",

}

TY - JOUR

T1 - A degree sum condition for long cycles passing through a linear forest

AU - Fujisawa, Jun

AU - Yamashita, Tomoki

PY - 2008/6/28

Y1 - 2008/6/28

N2 - Let G be a (k + m)-connected graph and F be a linear forest in G such that | E (F) | = m and F has at most k - 2 components of order 1, where k ≥ 2 and m ≥ 0. In this paper, we prove that if every independent set S of G with | S | = k + 1 contains two vertices whose degree sum is at least d, then G has a cycle C of length at least min { d - m, | V (G) | } which contains all the vertices and edges of F.

AB - Let G be a (k + m)-connected graph and F be a linear forest in G such that | E (F) | = m and F has at most k - 2 components of order 1, where k ≥ 2 and m ≥ 0. In this paper, we prove that if every independent set S of G with | S | = k + 1 contains two vertices whose degree sum is at least d, then G has a cycle C of length at least min { d - m, | V (G) | } which contains all the vertices and edges of F.

KW - Degree sum

KW - Linear forest

KW - Long cycle

UR - http://www.scopus.com/inward/record.url?scp=41549131212&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41549131212&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2007.05.005

DO - 10.1016/j.disc.2007.05.005

M3 - Article

VL - 308

SP - 2382

EP - 2388

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 12

ER -