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2002 | 22 | 1 | 123-148
Tytuł artykułu

Conditions for β-perfectness

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A β-perfect graph is a simple graph G such that χ(G') = β(G') for every induced subgraph G' of G, where χ(G') is the chromatic number of G', and β(G') is defined as the maximum over all induced subgraphs H of G' of the minimum vertex degree in H plus 1 (i.e., δ(H)+1). The vertices of a β-perfect graph G can be coloured with χ(G) colours in polynomial time (greedily).
The main purpose of this paper is to give necessary and sufficient conditions, in terms of forbidden induced subgraphs, for a graph to be β-perfect. We give new sufficient conditions and make improvements to sufficient conditions previously given by others. We also mention a necessary condition which generalizes the fact that no β-perfect graph contains an even hole.
Słowa kluczowe
Wydawca
Rocznik
Tom
22
Numer
1
Strony
123-148
Opis fizyczny
Daty
wydano
2002
otrzymano
2000-08-10
poprawiono
2001-07-03
Twórcy
  • University of Twente, Faculty of Mathematical Sciences, 7500 AE Enschede, The Netherlands
autor
  • Freiberg University, Faculty of Mathematics and Computer Sciences, 09596 Freiberg, Germany
Bibliografia
  • [1] L.W. Beineke, Characterizations of derived graphs, J. Combin. Theory 9 (1970) 129-135, doi: 10.1016/S0021-9800(70)80019-9.
  • [2] R.L. Brooks, On colouring the nodes of a network, Proc. Cambridge Phil. Soc. 37 (1941) 194-197, doi: 10.1017/S030500410002168X.
  • [3] M. Conforti, G. Cornuéjols, A. Kapoor and K. Vusković, Finding an even hole in a graph, in: Proceedings of the 38th Annual Symposium on Foundations of Computer Science (1997) 480-485, doi: 10.1109/SFCS.1997.646136.
  • [4] G.A. Dirac, On rigid circuit graphs, Abh. Math. Univ. Hamburg 25 (1961) 71-76, doi: 10.1007/BF02992776.
  • [5] P. Erdős and A. Hajnal, On the chromatic number of graphs and set-systems, Acta Math. Acad. Sci. Hungar. 17 (1966) 61-99, doi: 10.1007/BF02020444.
  • [6] C. Figueiredo and K. Vusković, A class of β-perfect graphs, Discrete Math. 216 (2000) 169-193, doi: 10.1016/S0012-365X(99)00240-X.
  • [7] H.-J. Finck and H. Sachs, Über eine von H.S. Wilf angegebene Schranke für die chromatische Zahl endlicher Graphen, Math. Nachr. 39 (1969) 373-386, doi: 10.1002/mana.19690390415.
  • [8] T.R. Jensen and B. Toft, Graph colouring problems (Wiley, New York, 1995).
  • [9] S.E. Markossian, G.S. Gasparian and B.A. Reed, β-perfect graphs, J. Combin. Theory (B) 67 (1996) 1-11, doi: 10.1006/jctb.1996.0030.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1163
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