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Vertex disjoint equivalent subgraphs of order 3
Author(s) -
Nakamigawa Tomoki
Publication year - 2007
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.20263
Subject(s) - combinatorics , mathematics , disjoint sets , vertex (graph theory) , discrete mathematics , cograph , graph , order (exchange) , line graph , 1 planar graph , finance , economics
Let k be a fixed integer at least 3. It is proved that every graph of order (2 k − 1 − 1/ k ) n + O (1) contains n vertex disjoint induced subgraphs of order k suchthat these subgraphs are equivalent to each other and they are equivalent to one of four graphs: a clique, an independent set, a star, or the complement of a star. In particular, by substituting 3 for k , it is proved that every graph of order 14 n /3 + O (1) contains n vertex disjoint induced subgraphs of order 3 such that they are equivalent to each other. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 159–166, 2007