Generalized colorings and avoidable orientations

• Autorzy: Jenő Szigeti , Zsolt Tuza
• Języki publikacji: EN

Abstrakty

EN

Gallai and Roy proved that a graph is k-colorable if and only if it has an orientation without directed paths of length k. We initiate the study of analogous characterizations for the existence of generalized graph colorings, where each color class induces a subgraph satisfying a given (hereditary) property. It is shown that a graph is partitionable into at most k independent sets and one induced matching if and only if it admits an orientation containing no subdigraph from a family of k+3 directed graphs.

Słowa kluczowe

EN

hereditary property; graph coloring

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1997
• Tom: 17
• Numer: 1
• Strony: 137-145

Daty

wydano

1997

otrzymano

1997-01-14

Twórcy

autor

Jenő Szigeti

• Mathematical Institute, University of Miskolc, H-3515 Miskolc-Egyetemváros, Hungary

autor

Zsolt Tuza

• Computer and Automation Institute, Hungarian Academy of Sciences, H-1111 Budapest, Kende u. 13-17, Hungary

Bibliografia

• [1] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discussiones Mathematicae Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.
• [2] J. Bucko, M. Frick, P. Mihók and R. Vasky, Uniquely partitionable graphs, Discussiones Mathematicae Graph Theory 17 (1997) 103-113, doi: 10.7151/dmgt.1043.
• [3] Y. Caro, Private communication, 1989.
• [4] T. Gallai, On directed paths and circuits, in: P. Erd os and G.O.H. Katona, eds., Theory of Graphs, Proc. Colloq. Math. Soc. János Bolyai, Tihany (Hungary) 1966 (Academic Press, San Diego, 1968) 115-118.
• [5] P. Mihók, Additive hereditary properties and uniquely partitionable graphs, in: Graphs, Hypergraphs and Matroids (Zielona Góra, 1985) 49-58.
• [6] G.J. Minty, A theorem on n-colouring the points of a linear graph, Amer. Math. Monthly 67 (1962) 623-624, doi: 10.2307/2310826.
• [7] R. Roy, Nombre chromatique et plus longs chemins d'un graphe, Revue AFIRO 1 (1967) 127-132.
• [8] Zs. Tuza, Graph coloring in linear time, J. Combin. Theory (B) 55 (1992) 236-243, doi: 10.1016/0095-8956(92)90042-V.
• [9] Zs. Tuza, Chromatic numbers and orientations, Unpublished manuscript, February 1993.
• [10] Zs. Tuza, Some remarks on the Gallai-Roy Theorem, in preparation.

Identyfikatory

DOI

10.7151/dmgt.1047