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June 2004 Hamiltonian cycles through a linear forest
Takeshi Sugiyama
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SUT J. Math. 40(2): 103-109 (June 2004). DOI: 10.55937/sut/1108749122

Abstract

Let G be a graph of order n. A graph is linear forest if every component is a path. Let S be a set of m edges of G that induces a linear forest. An edge xy E(G) is called an S-edge if xy S. An S-edge-length of a cycle in G is defined as the number of S-edges that it contains. We prove that if the degree sum in G of every pair of nonadjacent vertices of G is at least n + m, then G contains hamiltonian cycles of every S-edge-length between 0 and |S|.

Acknowledgments

I would like to thank Dr. Tomoki Yamashita for stimulating discussions and important suggestion. I am thankful to the referee for carefully reading the manuscript and many helpful suggestions.

Citation

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Takeshi Sugiyama. "Hamiltonian cycles through a linear forest." SUT J. Math. 40 (2) 103 - 109, June 2004. https://doi.org/10.55937/sut/1108749122

Information

Received: 8 July 2004; Revised: 13 December 2004; Published: June 2004
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1108749122

Subjects:
Primary: 05C38

Keywords: Hamiltonian cycle , linear forest

Rights: Copyright © 2004 Tokyo University of Science

Vol.40 • No. 2 • June 2004
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