Open AccessHamiltonian claw-free graphs involving induced cycles
Author(s) -
Jianxing Yin,
Liming Xiong
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1634/1/012069
Subject(s) - hamiltonian path , hamiltonian (control theory) , combinatorics , mathematics , claw , hamiltonian path problem , pancyclic graph , graph , discrete mathematics , line graph , pathwidth , mathematical optimization , structural engineering , engineering
The hamiltonian problem is an important topic in structural graph theory, which is closely related to Four Color Problem. Hence lots of graph scholars are dedicated to this topic. There are many authors working for finding some sufficient conditions for hamiltonian property of graphs. Let G be a claw-free graph with n vertices and δ ( G )≥3. In this paper, we show that if G has an induced cycle of length more than (4 n – 2 δ ( G )–4)( δ ( G )+2) −1 , then G is hamiltonian. The result is best possible if δ G is 3 or 4.