Some maximum multigraphs and edge/vertex distance colourings

• Autorzy: Zdzisław Skupień
• Języki publikacji: EN

Abstrakty

EN

Shannon-Vizing-type problems concerning the upper bound for a distance chromatic index of multigraphs G in terms of the maximum degree Δ(G) are studied. Conjectures generalizing those related to the strong chromatic index are presented. The chromatic d-index and chromatic d-number of paths, cycles, trees and some hypercubes are determined. Among hypercubes, however, the exact order of their growth is found.

Słowa kluczowe

EN

(strong) chromatic index; chromatic number; matching; hypercube; error-correcting code; asymptotics

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C35: Extremal problems
• 94B05: Linear codes, general

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1995
• Tom: 15
• Numer: 1
• Strony: 89-106

Daty

wydano

1995

otrzymano

1994-11-30

Twórcy

autor

Zdzisław Skupień

• Institute of Math. AGH, al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

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• [2] J.C. Bermond, J. Bond, M. Paoli and C. Peyrat, Graphs and interconnection networks: diameter and vulnerability, in: Surveys in Combinatorics, Proc. Ninth British Combin. Conf. (London Math. Soc., Lect. Notes Series 82, 1983) 1-30.
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• [4] R.J. Faudree, A. Gyarfas, R.H. Schelp and Zs. Tuza, Induced matchings in bipartite graphs, Discrete Math. 78 (1989) 83-87, doi: 10.1016/0012-365X(89)90163-5.
• [5] R.J. Faudree, R.H. Schelp, A. Gyarfas and Zs. Tuza, The strong chromatic index of graphs, Ars Combinat. 29-B (1990) 205-211.
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• [9] F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes (North-Holland, Amsterdam et al., 1981).
• [10] C.E. Shannon, A theorem on coloring the lines of a network, J. Math. Phys. 28 (1949) 148-151.
• [11] E. Sidorowicz and Z. Skupień, A joint article in preparation.
• [12] Z. Skupień, Some maximum multigraphs and chromatic d-index, in: U. Faigle and C. Hoede, eds., 3rd Twente Workshop on Graphs and Combinatorial Optimization (Fac. Appl. Math. Univ. Twente, Enschede, 1993) 173-175.
• [13] V.G. Vizing, Chromatic class of a multigraph [Russian], Kibernetika 3 (1965) 29-39.
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Identyfikatory

DOI

10.7151/dmgt.1010