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
SN - 0012-365X
VL - 308
SP - 2382
EP - 2388
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 12
ER -