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Vertex disjoint equivalent subgraphs of order 3

✍ Scribed by Tomoki Nakamigawa

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
129 KB
Volume
56
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

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 such
that 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

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We study the fusion rules of a vertex operator algebra W 0 , which is a VOA ‫ޒ‬ over the real number field ‫ޒ‬ and has a positive definite invariant bilinear form, Ž . q and such that its complexification ‫ރ‬W 0 is a direct sum of the 3-state Potts ‫ޒ‬ 4 4 Ž . Ž . model L , 0 and its module L , 3 .