Title
Document Type
Article
Publication Date
2000
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
DOI
http://dx.doi.org/10.1556/SScMath.38.2001.1-4.8
Required Publisher's Statement
© Akadémiai Kiadó Zrt.
Recommended Citation
Bollobás, Béla and Sarkar, Amites, "Paths in Graphs" (2000). Mathematics Faculty Publications. 81.
https://cedar.wwu.edu/math_facpubs/81
Subjects - Topical (LCSH)
Paths and cycles (Graph theory)
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf
Comments
This is the authors' refereed version of the article.