Summary
For a given approximate coloring algorithm a graph G is said to be hard-to-color (HC) if every implementation of the algorithm uses more colors than the chromatic number. For a collection of such algorithms G is called a benchmark if it is HC for every algorithm in the collection. In the paper we study the performance of six sequential algorithms when used in two models of coloring: classical and chromatic sum. We give the smallest HC graph for each of them and two collective benchmarks for both models of coloring.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Babel, L.; Tinhofer, G. (1994): Hard-to-color graphs for connected sequential colorings, Ann. Disc. Math. 51, 1994, pp. 3–25.
Bar-Noy, A.; Kortsarz, G. (1998): The minimum color sum of bipartite graphs, J. Algorithms 28, 1998, pp. 339–365.
Brélaz, D. (1979): New methods to color the vertices of a graph, Comm. ACM 22, 1979, pp. 251–256
Hansen, P.; Kuplinsky, J. (1990): Slightly hard-to-color graphs. Cong. Numer. 78, 1990, pp. 81–98.
Hansen, P.; Kuplinsky, J. (1991): The smallest hard-to-color graph, Disc. Math. 98, 1991, pp.199–212.
Janczewski, R.; Kubale, M; Manuszewski, K.; Piwakowski, K. (2000): The smallest hard-to-color graph for algorithm DSATUR (to appear in Disc. Math).
Johnson, D.S. (1974): Worst-case behavior of graph coloring algorithms, in: Proc. 5th S.E. Conf. on Combinatorics, Graph Theory and Computing, Utilitas Math., Winnipeg, 1974, pp. 513–527.
Johnson, D.S.; Trick, M.A. (eds.) (1996): Cliques, Coloring and Satisfiability, DIMACS Series in Discrete Mathematic and Theoretical Computer Science 26, 1996.
Kubale, M; Manuszewski, K. (1999): The smallest hard-to-color graphs for the classical, total and strong colorings of vertices, Contr. Cyber. 28, 1999.
Kubale, M; Pakulski, J. (1994): A catalogue of the smallest hard-to-color graphs, in: Proc. Int. Conf. Operations Research′94, Berlin, 1994, pp. 133–138.
Kubale, M.; Pakulski, J.K.; Piwakowski, K. (1997): The smallest hard-to-color graph for the SL algorithm, Dics. Math. 164, 1997, pp. 197–212.
Manuszewski, K. (1998): Graphs Algorithmically Hard to Color, Ph.D. Thesis, Technical University of Gdańsk (in Polish).
Matula, D.W.; Marble, G.; Isaacson, D. (1972): Graph coloring algorithms, in: Graph Theory and Computing, Academic Press, New York, 1972, pp. 109–122.
Welsh, D.J.; Powell, M.B. (1967): An upper bound for the chromatic number of a graph and its application to timetabling problem, Comp. J. 10, 1967, pp. 85–86.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kubale, M., Manuszewski, K. (2000). The Smallest Hard-to-Color Graphs for Sequential Coloring Algorithms. In: Inderfurth, K., Schwödiauer, G., Domschke, W., Juhnke, F., Kleinschmidt, P., Wäscher, G. (eds) Operations Research Proceedings 1999. Operations Research Proceedings 1999, vol 1999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58300-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-58300-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67094-0
Online ISBN: 978-3-642-58300-1
eBook Packages: Springer Book Archive