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Competitive inheritance and limitedness of graphs
Author(s) -
Wang Chi
Publication year - 1995
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190190308
Subject(s) - mathematics , combinatorics , conjecture , inheritance (genetic algorithm) , graph , discrete mathematics , competition (biology) , ecology , biochemistry , chemistry , biology , gene
The study of competition number of graphs has brought many interesting problems to graph theory and combinatorics. However, little is known about what makes the competition number of a graph small or large. In this paper, we introduce competitive inheritance and limitedness of graphs. We show that most graphs studied in the literature of competition graphs possess the inheritance property on their competition number. We characterize the limitedness of graphs on competition number by forbidden induced subgraphs. Our results also prove a conjecture of Opsut on competition number for a new class of graphs. © 1995 John Wiley & Sons, Inc.