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Third case of the cyclic coloring conjecture
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Hebdige, Michael and Král', Daniel (2015) Third case of the cyclic coloring conjecture. In: The Eight European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2015, Bergen, Norway, 31 Aug 4 Sep 2015. Published in: Electronic Notes in Discrete Mathematics, 49 pp. 11-15. doi:10.1016/j.endm.2015.06.003 ISSN 1571-0653.
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Official URL: http://dx.doi.org/10.1016/j.endm.2015.06.003
Abstract
The Cyclic Coloring Conjecture of Ore and Plummer from 1969 asserts that the vertices of every plane graph with maximum face size Δ⁎ can be colored using at most ⌊3Δ⁎/2⌋ colors in such a way that no face is incident with two vertices of the same color. The Cyclic Coloring Conjecture has been proven only for two values of Δ⁎: the case Δ⁎=3 is equivalent to the Four Color Theorem and the case Δ⁎=4 is equivalent to Borodin's Six Color Theorem, which says that every graph that can be drawn in the plane with each edge crossed by at most one other edge is 6-colorable. We prove the case Δ⁎=6 of the conjecture.
Item Type: | Conference Item (Poster) | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Mathematics |
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Journal or Publication Title: | Electronic Notes in Discrete Mathematics | ||||
Publisher: | Elsevier BV | ||||
ISSN: | 1571-0653 | ||||
Official Date: | 12 November 2015 | ||||
Dates: |
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Volume: | 49 | ||||
Page Range: | pp. 11-15 | ||||
DOI: | 10.1016/j.endm.2015.06.003 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Conference Paper Type: | Poster | ||||
Title of Event: | The Eight European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2015 | ||||
Type of Event: | Conference | ||||
Location of Event: | Bergen, Norway | ||||
Date(s) of Event: | 31 Aug 4 Sep 2015 | ||||
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