First-fit coloring on interval graphs has performance ratio at least 5

Henry Kierstead; David A. Smith; W. T. Trotter

doi:10.1016/j.ejc.2015.05.015

First-fit coloring on interval graphs has performance ratio at least 5

Henry Kierstead, David A. Smith, W. T. Trotter

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15 Scopus citations

Abstract

First-fit is the online graph coloring algorithm that considers vertices one at a time in some order and assigns each vertex the least positive integer not used already on a neighbor. The maximum number of colors used by first-fit on graph G over all vertex orders is denoted χ_FF(G).The exact value of R:=supGχFF(G)ω(G) over interval graphs G is unknown. Pemmaraju, Raman, and Varadarajan (2004) proved R≤. 10, and this can be improved to 8. Witsenhausen (1976) and Chrobak and Ślusarek (1988) showed R≥. 4, and Ślusarek (1993) improved this to 4.45. We prove R≥. 5.

Original language	English (US)
Pages (from-to)	236-254
Number of pages	19
Journal	European Journal of Combinatorics
Volume	51
DOIs	https://doi.org/10.1016/j.ejc.2015.05.015
State	Published - Jan 1 2016

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2015.05.015

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title = "First-fit coloring on interval graphs has performance ratio at least 5",

abstract = "First-fit is the online graph coloring algorithm that considers vertices one at a time in some order and assigns each vertex the least positive integer not used already on a neighbor. The maximum number of colors used by first-fit on graph G over all vertex orders is denoted χFF(G).The exact value of R:=supGχFF(G)ω(G) over interval graphs G is unknown. Pemmaraju, Raman, and Varadarajan (2004) proved R≤. 10, and this can be improved to 8. Witsenhausen (1976) and Chrobak and {\'S}lusarek (1988) showed R≥. 4, and {\'S}lusarek (1993) improved this to 4.45. We prove R≥. 5.",

author = "Henry Kierstead and Smith, {David A.} and Trotter, {W. T.}",

note = "Funding Information: The research of first and second authors was supported in part by NSF grant DMS-0901520 . Publisher Copyright: {\textcopyright} 2015 Elsevier Ltd.",

year = "2016",

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doi = "10.1016/j.ejc.2015.05.015",

language = "English (US)",

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T1 - First-fit coloring on interval graphs has performance ratio at least 5

AU - Kierstead, Henry

AU - Smith, David A.

AU - Trotter, W. T.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - First-fit is the online graph coloring algorithm that considers vertices one at a time in some order and assigns each vertex the least positive integer not used already on a neighbor. The maximum number of colors used by first-fit on graph G over all vertex orders is denoted χFF(G).The exact value of R:=supGχFF(G)ω(G) over interval graphs G is unknown. Pemmaraju, Raman, and Varadarajan (2004) proved R≤. 10, and this can be improved to 8. Witsenhausen (1976) and Chrobak and Ślusarek (1988) showed R≥. 4, and Ślusarek (1993) improved this to 4.45. We prove R≥. 5.

AB - First-fit is the online graph coloring algorithm that considers vertices one at a time in some order and assigns each vertex the least positive integer not used already on a neighbor. The maximum number of colors used by first-fit on graph G over all vertex orders is denoted χFF(G).The exact value of R:=supGχFF(G)ω(G) over interval graphs G is unknown. Pemmaraju, Raman, and Varadarajan (2004) proved R≤. 10, and this can be improved to 8. Witsenhausen (1976) and Chrobak and Ślusarek (1988) showed R≥. 4, and Ślusarek (1993) improved this to 4.45. We prove R≥. 5.

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First-fit coloring on interval graphs has performance ratio at least 5

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