On-line coloring of $I_s$-free graphs

An on-line vertex coloring algorithm receives vertices of a graph in some externally determined order. Each new vertex is presented together with a set of the edges connecting it to the previously presented vertices. As a vertex is presented, the algorithm assigns it a color which cannot be changed...

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Veröffentlicht in:Discrete mathematics and theoretical computer science Jg. DMTCS Proceedings vol. AF,...; H. Proceedings; S. 61 - 68
Hauptverfasser: Cieslik, Iwona, Kozik, Marcin, Micek, Piotr
Format: Journal Article Tagungsbericht
Sprache:Englisch
Veröffentlicht: DMTCS 01.01.2005
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Schriftenreihe:DMTCS Proceedings
Schlagworte:
[info.info-hc] computer science [cs]/human-computer interaction [cs.hc]
[info.info-lo] computer science [cs]/logic in computer science [cs.lo]
[info.info-sc] computer science [cs]/symbolic computation [cs.sc]
Computer Science
graph coloring
Human-Computer Interaction
Logic in Computer Science
on-line algorithm
planar graph
Symbolic Computation
on-line algorithm
graph coloring
planar graph
ISSN:1365-8050, 1462-7264, 1365-8050
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:An on-line vertex coloring algorithm receives vertices of a graph in some externally determined order. Each new vertex is presented together with a set of the edges connecting it to the previously presented vertices. As a vertex is presented, the algorithm assigns it a color which cannot be changed afterwards. The on-line coloring problem was addressed for many different classes of graphs defined in terms of forbidden structures. We analyze the class of $I_s$-free graphs, i.e., graphs in which the maximal size of an independent set is at most $s-1$. An old Szemerédi's result implies that for each on-line algorithm A there exists an on-line presentation of an $I_s$-free graph $G$ forcing A to use at least $\frac{s}{2}χ ^{(G)}$ colors. We prove that any greedy algorithm uses at most $\frac{s}{2}χ^{(G)}$ colors for any on-line presentation of any $I_s$-free graph $G$. Since the class of co-planar graphs is a subclass of $I_5$-free graphs all greedy algorithms use at most $\frac{5}{2}χ (G)$ colors for co-planar $G$'s. We prove that, even in a smaller class, this is an almost tight bound.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.3472