Document Type

Article

Publication Date

2001

Keywords

Maximal number of paths of lengths s in a graph with m edges, maximal number of subgraphs isomorphic to a given graph

Abstract

We prove that if 10 ≦ (k2) ≦ m < (k+12) then the number of paths of length three in a graph G of size m is at most 2m(m – k)(k - 2)/k. Equality is attained if G is the union of Kk and isolated vertices. We also give asymptotically best possible bounds for the maximal number of paths of length s, for arbitrary s, in graphs of size m. Lastly, we discuss the more general problem of maximizing the number of subgraphs isomorphic to a given graph H in graphs of size m.

Publication Title

Studia Scientiarum Mathematicarum Hungarica

Volume

38

Issue

1-4

First Page

115

Last Page

137

Required Publisher's Statement

© Akadémiai Kiadó Zrt.

DOI: http://dx.doi.org/10.1556/SScMath.38.2001.1-4.8

Comments

This is the authors' refereed version of the article.

Language

English

Format

application/pdf

Included in

Mathematics Commons

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