The competition number of the complement of a cycle

In this paper, we compute the competition number of the complement of a cycle. It is well-known that the competition number of a cycle of length at least 4 is two while the competition number of a cycle of length 3 is one. Characterizing a graph by its competition number has been one of important re...

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Published inDiscrete Applied Mathematics Vol. 161; no. 12; pp. 1755 - 1760
Main Authors Kim, Suh-Ryung, Park, Boram, Sano, Yoshio
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2013
Subjects
Circulant graph
Competition
Competition graph
Competition number
Complement
Computation
Edge clique cover
Graphs
Mathematical models
The complement of a cycle
Circulant graph
Competition number
Edge clique cover
Competition graph
The complement of a cycle
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Abstract In this paper, we compute the competition number of the complement of a cycle. It is well-known that the competition number of a cycle of length at least 4 is two while the competition number of a cycle of length 3 is one. Characterizing a graph by its competition number has been one of important research problems in the study of competition graphs, and competition numbers of various interesting families of graphs have been found. We thought that it is worthy of computing the competition number of the complement of a cycle. In the meantime, the observation that the complement of an odd cycle of length at least 5 is isomorphic to a circulant graph led us to compute the competition number of a large family of circulant graphs. In fact, those circulant graphs satisfy the long lasting Opsut’s conjecture stating that the competition number of a locally cobipartite graph is at most two.
AbstractList In this paper, we compute the competition number of the complement of a cycle. It is well-known that the competition number of a cycle of length at least 4 is two while the competition number of a cycle of length 3 is one. Characterizing a graph by its competition number has been one of important research problems in the study of competition graphs, and competition numbers of various interesting families of graphs have been found. We thought that it is worthy of computing the competition number of the complement of a cycle. In the meantime, the observation that the complement of an odd cycle of length at least 5 is isomorphic to a circulant graph led us to compute the competition number of a large family of circulant graphs. In fact, those circulant graphs satisfy the long lasting Opsut’s conjecture stating that the competition number of a locally cobipartite graph is at most two.
In this paper, we compute the competition number of the complement of a cycle. It is well-known that the competition number of a cycle of length at least 4 is two while the competition number of a cycle of length 3 is one. Characterizing a graph by its competition number has been one of important research problems in the study of competition graphs, and competition numbers of various interesting families of graphs have been found. We thought that it is worthy of computing the competition number of the complement of a cycle. In the meantime, the observation that the complement of an odd cycle of length at least 5 is isomorphic to a circulant graph led us to compute the competition number of a large family of circulant graphs. In fact, those circulant graphs satisfy the long lasting Opsutas conjecture stating that the competition number of a locally cobipartite graph is at most two.
Author Park, Boram
Kim, Suh-Ryung
Sano, Yoshio
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Cites_doi 10.1016/0166-218X(83)90086-0
10.7151/dmgt.1506
10.1137/0603043
10.4134/JKMS.2011.48.4.691
10.1016/j.dam.2008.04.009
10.1016/j.disc.2009.06.016
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Keywords Circulant graph
Competition number
Edge clique cover
Competition graph
The complement of a cycle
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Snippet In this paper, we compute the competition number of the complement of a cycle. It is well-known that the competition number of a cycle of length at least 4 is...
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SubjectTerms Circulant graph
Competition
Competition graph
Competition number
Complement
Computation
Edge clique cover
Graphs
Mathematical models
The complement of a cycle
Title The competition number of the complement of a cycle
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