Long cycles in triangle-free graphs with prescribed independence number and connectivity

Authors:
Hikoe Enomoto;Atsushi Kaneko;Akira Saito;Bing Wei
Affiliations:
Department of Mathematics, Keio University, Hiyoshi 3-14-1 Kohoku-Ku, Yokohama 223-8522, Japan;Department of Electronic Engineering, Kogakuin University, Nishi-Shinjuku 1-24-2, Shinjuku-Ku, Tokyo 163-8677, Japan;Department of Applied Mathematics, Nihon University, Sakurajosui 3-25-40, Setagaya-Ku, Tokyo 156-8550, Japan;Institute of Systems Science, Academia Sinica, Beijing 100080, China
Venue:
Journal of Combinatorial Theory Series B
Year:
2004

Citing 4
Cited 1

Graphs & digraphs (2nd ed.)

Graphs & digraphs (2nd ed.)
Longest cycles in triangle-free graphs

Journal of Combinatorial Theory Series B
Cycles in graphs with prescribed stability number and connectivity

Journal of Combinatorial Theory Series B
The Chvátal-Erdős condition for cycles in triangle-free graphs

Discrete Mathematics

Chvátal---Erdős Theorem: Old Theorem with New Aspects

Computational Geometry and Graph Theory

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Abstract

The Chvátal-Erdös theorem says that a 2-connected graph with α(G)≤κ(G) is hamiltonian. We extend this theorem for triangle-free graphs. We prove that if G is a 2-connected triangle-free graph of order n with α(G)≤2κ(G) - 2, then every longest cycle in G is dominating, and G has a cycle of length at least min{n - α(G) + κ(G), n}.