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Title: Edit distance measure for graphs (English)
Author: Dzido, Tomasz
Author: Krzywdziński, Krzysztof
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 65
Issue: 3
Year: 2015
Pages: 829-836
Summary lang: English
Category: math
Summary: In this paper, we investigate a measure of similarity of graphs similar to the Ramsey number. We present values and bounds for $g(n,l)$, the biggest number $k$ guaranteeing that there exist $l$ graphs on $n$ vertices, each two having edit distance at least $k$. By edit distance of two graphs $G$, $F$ we mean the number of edges needed to be added to or deleted from graph $G$ to obtain graph $F$. This new extremal number $g(n, l)$ is closely linked to the edit distance of graphs. Using probabilistic methods we show that $g(n, l)$ is close to $\frac 12\binom n2$ for small values of $l>2$. We also present some exact values for small $n$ and lower bounds for very large $l$ close to the number of non-isomorphic graphs of $n$ vertices. (English)
Keyword: extremal graph problem
Keyword: similarity of graphs
MSC: 05C35
MSC: 05C75
idZBL: Zbl 06537695
idMR: MR3407608
DOI: 10.1007/s10587-015-0211-4
Date available: 2015-10-04T18:22:42Z
Last updated: 2020-07-03
Stable URL:
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