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

Jun Fujisawa, Tomoki Yamashita

Research output: Contribution to journalArticle


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
Issue number12
Publication statusPublished - 2008 Jun 28
Externally publishedYes



  • Degree sum
  • Linear forest
  • Long cycle

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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