[r, s, t]-colourings of paths

• Autorzy: Salvador Villa M. , Schiermeyer I.
• Języki publikacji: EN

Abstrakty

EN

The concept of [r, s, t]-colourings was recently introduced by Hackmann, Kemnitz and Marangio [3] as follows: Given non-negative integers r, s and t, an [r, s, t]-colouring of a graph G = (V(G), E(G)) is a mapping c from V(G) ∪ E(G) to the colour set {1, 2,..., k} such that ‌c(vi) - c(vj)‌ ≥ r for every two adjacent vertices vi, vj, ‌c(ei) - c(ej)‌ ≥ s for every two adjacent edges ei, ej, and ‌c(vi) - c(ej)‌ ≥ t for all pairs of incident vertices and edges, respectively. The [r, s, t]-chromatic number Xr,s,t(G) of G is defined to be the minimum k such that G admits an [r, s, t]-colouring. In this paper, we determine the [r, s, t]-chromatic number for paths.

Słowa kluczowe

EN

total colouring; paths

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2007
• Tom: Vol. 27, no. 1
• Strony: 131--149
• Opis fizyczny: Bibliogr. 6 poz., rys., tab.

Twórcy

autor

Salvador Villa M.

autor

Schiermeyer I.

• Graduiertenkolleg "Räumliche Statistik", Technische Universität Bergakademie Freiberg, 09596 Freiberg,

Bibliografia

• [1] Brooks R.L., On colouring the nodes of a network, Proc. Cambridge Phil. Soc. 37 (1941), 194-197.
• [2] T.R. Jensen, B. Toft, Graph Coloring Problems, Wiley-Interscience, New York 1995.
• [3] A. Kemnitz, M. Marangio, [r,s,t]-Colorings of Graphs, Discrete Math., to appear.
• [4] V.G. Vizing, On an estimate of the chromatic class of a p-graph, Diskret. Analiz. 3 (1964), 25-30.
• [5] D.B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall (2001).
• [6] H.P. Yap, Total Colourings of Graphs, Springer (Lecture Notes in Mathematics; 1623) (1996).