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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
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Category: math
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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
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Date available: 2015-10-04T18:22:42Z
Last updated: 2017-10-02
Stable URL: http://hdl.handle.net/10338.dmlcz/144446
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Reference: [4] Axenovich, M., Kézdy, A., Martin, R.: On the editing distance of graphs.J. Graph Theory 58 (2008), 123-138. Zbl 1156.05027, MR 2407000, 10.1002/jgt.20296
Reference: [5] Balogh, J., Martin, R.: Edit distance and its computation.Electron. J. Comb. (electronic only) 15 (2008), Research Paper R20, 27 pages. Zbl 1159.05030, MR 2383440
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Reference: [7] Chung, F. R. K., Erdős, P., Graham, R. L.: Minimal decompositions of graphs into mutually isomorphic subgraphs.Combinatorica 1 (1981), 13-24. Zbl 0491.05049, MR 0602412, 10.1007/BF02579173
Reference: [8] Wet, P. O. de: Constructing a large number of nonisomorphic graphs of order $n$.Morehead Electronic Journal of Applicable Mathematics 1 (2001), 2 pages.
Reference: [9] Dzido, T., Krzywdziński, K.: On a local similarity of graphs.Discrete Math. 338 (2015), 983-989. MR 3318633, 10.1016/j.disc.2015.01.016
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