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Anti-Ramsey numbers of doubly edge-critical graphs
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Jiang, Tao and Pikhurko, Oleg (2009) Anti-Ramsey numbers of doubly edge-critical graphs. Journal of Graph Theory, Vol.61 (No.3). pp. 210-218. doi:10.1002/jgt.20380 ISSN 0364-9024.
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Official URL: http://dx.doi.org/10.1002/jgt.20380
Abstract
Given a graph H and a positive integer n, Anti-Ramsey number AR(n, H) is the maximum number of colors in an edge-coloring of Kn that contains no polychromatic copy of H. The anti-Ramsey numbers were introduced in the 1970s by Erdős, Simonovits, and Sós, who among other things, determined this function for cliques. In general, few exact values of AR(n, H) are known. Let us call a graph Hdoubly edge-critical if χ(H−e)≥p+ 1 for each edge e∈E(H) and there exist two edges e1, e2 of H for which χ(H−e1−e2)=p. Here, we obtain the exact value of AR(n, H) for any doubly edge-critical H when n⩾n0(H) is sufficiently large. A main ingredient of our proof is the stability theorem of Erdős and Simonovits for the Turán problem. © 2009 Wiley Periodicals, Inc. J Graph Theory 61: 210–218, 2009
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Journal of Graph Theory | ||||
| Publisher: | John Wiley & Sons Ltd. | ||||
| ISSN: | 0364-9024 | ||||
| Official Date: | July 2009 | ||||
| Dates: |
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| Volume: | Vol.61 | ||||
| Number: | No.3 | ||||
| Page Range: | pp. 210-218 | ||||
| DOI: | 10.1002/jgt.20380 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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