✦ LIBER ✦

A generalization of chromatic index

✍ Scribed by E. Sampathkumar; G.D. Kamath

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 261 KB
Volume: 124
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90088-4

No coin nor oath required. For personal study only.

✦ Synopsis

Let G = (V, E) be a graph and k > 2 an integer. The general chromatic index x;(G) of G is the minimum order of a partition P of E such that for any set F in P every component in the subgraph (F) induced by F has size at most k-1. This paper initiates a study of x;(G) and generalizes some known results on chromatic index.

📜 SIMILAR VOLUMES

A generalized construction of chromatic

A generalized construction of chromatic index critical graphs from bipartite graphs

✍ Michael Plantholt 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 378 KB

W e prove that any graph with maximum degree n which can be obtained by removing exactly 2n -1 edges from the join K? -K, ,, is n-critical This generalizes special constructions of critical graphs by S Fiorini and H P Yap, and suggests a possible extension of another general construction due to Yap

A Symmetric Function Generalization of t

A Symmetric Function Generalization of the Chromatic Polynomial of a Graph

✍ R.P. Stanley 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 932 KB

For a finite graph \(G\) with \(d\) vertices we define a homogeneous symmetric function \(X_{4 ;}\) of degree \(d\) in the variables \(x_{1}, x_{2}, \ldots\). If we set \(x_{1}=\cdots=x_{n}=1\) and all other \(x_{t}=0\), then we obtain \(Z_{1}(n)\), the chromatic polynomial of (; evaluated at \(n\).

A construction of chromatic index critic

A construction of chromatic index critical graphs

✍ Hian Poh Yap 📂 Article 📅 1981 🏛 John Wiley and Sons 🌐 English ⚖ 219 KB

## Abstract We prove that if __K__ is an undirected, simple, connected graph of even order which is of class one, regular of degree __p__ ≥ 2 and such that the subgraph induced by any three vertices is either connected or null, then any graph __G__ obtained from __K__ by splitting any vertex is __p

The skew chromatic index of a graph

✍ Marsha F Foregger 📂 Article 📅 1984 🏛 Elsevier Science 🌐 English ⚖ 594 KB

We define a skew edge coloring of a graph to be a set of two edge colorings such that no two edges are assigned the same unordered pair of colors. The skew chromatic index s(G) is the minimum number of colors required for a skew edge coloring of G. We show that this concept is closely related to tha

A note concerning the chromatic index of

A note concerning the chromatic index of multigraphs

✍ A. J. W. Hilton; Bill Jackson 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 214 KB

We improve an upper bound for the chromatic index of a multigraph due to Andersen and Gol'dberg. As a corollary w e deduce that if no t w o edges of multiplicity at least t w o in G are adjacent, then ,y'(G) s A ( G ) + 1. In addition w e generalize results concerning the structure of critical graph

The List Chromatic Index of a Bipartite

The List Chromatic Index of a Bipartite Multigraph

✍ F. Galvin 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 243 KB

For a bipartite multigraph, the list chromatic index is equal to the chromatic index (which is, of course, the same as the maximum degree). This generalizes Janssen's result on complete bipartite graphs \(K_{m, n}\) with \(m \neq n\); in the case of \(K_{n, n}\) it answers a question of Dinitz. (The