TY - JOUR

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

AU - Fujisawa, Jun

AU - Yamashita, Tomoki

N1 - Funding Information:
This work was partially supported by the JSPS Research Fellowships for Young Scientists (to J.F.) and by the 21st Century COE Program; Integrative Mathematical Sciences: Progress in Mathematics Motivated by Social and Natural Sciences (to T.Y.).

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

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U2 - 10.1016/j.disc.2007.05.005

DO - 10.1016/j.disc.2007.05.005

M3 - Article

AN - SCOPUS:41549131212

VL - 308

SP - 2382

EP - 2388

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 12

ER -