Unique-maximum and conflict-free coloring for hypergraphs and tree graphs

Panagiotis Cheilaris; Balázs Keszegh; Dömötör Pálvölgyi

doi:10.1007/978-3-642-27660-6_16

Unique-maximum and conflict-free coloring for hypergraphs and tree graphs

Panagiotis Cheilaris
, Balázs Keszegh
, Dömötör Pálvölgyi

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

We investigate the relationship between two kinds of vertex colorings of hypergraphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every hyperedge of the hypergraph the maximum color in the hyperedge occurs in only one vertex of the hyperedge. In a conflict-free coloring, in every hyperedge of the hypergraph there exists a color in the hyperedge that occurs in only one vertex of the hyperedge. We define corresponding unique-maximum and conflict-free chromatic numbers and investigate their relationship in arbitrary hypergraphs. Then, we concentrate on hypergraphs that are induced by simple paths in tree graphs.

Original language	English
Title of host publication	SOFSEM 2012
Subtitle of host publication	Theory and Practice of Computer Science - 38th Conference on Current Trends in Theory and Practice of Computer Science, Proceedings
Pages	190-201
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-27660-6_16
State	Published - 25 Jan 2012
Event	38th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2012 - Spindleruv Mlyn, Czech Republic Duration: 21 Jan 2012 → 27 Jan 2012

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7147 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	38th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2012
Country/Territory	Czech Republic
City	Spindleruv Mlyn
Period	21/01/12 → 27/01/12

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-642-27660-6_16

Cite this

Cheilaris, P., Keszegh, B., & Pálvölgyi, D. (2012). Unique-maximum and conflict-free coloring for hypergraphs and tree graphs. In SOFSEM 2012: Theory and Practice of Computer Science - 38th Conference on Current Trends in Theory and Practice of Computer Science, Proceedings (pp. 190-201). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7147 LNCS). https://doi.org/10.1007/978-3-642-27660-6_16

Cheilaris, Panagiotis ; Keszegh, Balázs ; Pálvölgyi, Dömötör. / Unique-maximum and conflict-free coloring for hypergraphs and tree graphs. SOFSEM 2012: Theory and Practice of Computer Science - 38th Conference on Current Trends in Theory and Practice of Computer Science, Proceedings. 2012. pp. 190-201 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We investigate the relationship between two kinds of vertex colorings of hypergraphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every hyperedge of the hypergraph the maximum color in the hyperedge occurs in only one vertex of the hyperedge. In a conflict-free coloring, in every hyperedge of the hypergraph there exists a color in the hyperedge that occurs in only one vertex of the hyperedge. We define corresponding unique-maximum and conflict-free chromatic numbers and investigate their relationship in arbitrary hypergraphs. Then, we concentrate on hypergraphs that are induced by simple paths in tree graphs.",

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Cheilaris, P, Keszegh, B & Pálvölgyi, D 2012, Unique-maximum and conflict-free coloring for hypergraphs and tree graphs. in SOFSEM 2012: Theory and Practice of Computer Science - 38th Conference on Current Trends in Theory and Practice of Computer Science, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7147 LNCS, pp. 190-201, 38th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2012, Spindleruv Mlyn, Czech Republic, 21/01/12. https://doi.org/10.1007/978-3-642-27660-6_16

Unique-maximum and conflict-free coloring for hypergraphs and tree graphs. / Cheilaris, Panagiotis; Keszegh, Balázs; Pálvölgyi, Dömötör.
SOFSEM 2012: Theory and Practice of Computer Science - 38th Conference on Current Trends in Theory and Practice of Computer Science, Proceedings. 2012. p. 190-201 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7147 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - We investigate the relationship between two kinds of vertex colorings of hypergraphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every hyperedge of the hypergraph the maximum color in the hyperedge occurs in only one vertex of the hyperedge. In a conflict-free coloring, in every hyperedge of the hypergraph there exists a color in the hyperedge that occurs in only one vertex of the hyperedge. We define corresponding unique-maximum and conflict-free chromatic numbers and investigate their relationship in arbitrary hypergraphs. Then, we concentrate on hypergraphs that are induced by simple paths in tree graphs.

AB - We investigate the relationship between two kinds of vertex colorings of hypergraphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every hyperedge of the hypergraph the maximum color in the hyperedge occurs in only one vertex of the hyperedge. In a conflict-free coloring, in every hyperedge of the hypergraph there exists a color in the hyperedge that occurs in only one vertex of the hyperedge. We define corresponding unique-maximum and conflict-free chromatic numbers and investigate their relationship in arbitrary hypergraphs. Then, we concentrate on hypergraphs that are induced by simple paths in tree graphs.

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Cheilaris P, Keszegh B, Pálvölgyi D. Unique-maximum and conflict-free coloring for hypergraphs and tree graphs. In SOFSEM 2012: Theory and Practice of Computer Science - 38th Conference on Current Trends in Theory and Practice of Computer Science, Proceedings. 2012. p. 190-201. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-27660-6_16

Unique-maximum and conflict-free coloring for hypergraphs and tree graphs

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