On the total coloring of certain graphs
β Scribed by M. Rosenfeld
- Book ID
- 112888987
- Publisher
- The Hebrew University Magnes Press
- Year
- 1971
- Tongue
- English
- Weight
- 248 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0021-2172
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
AND Bruce Reed Department of Combinatorics and Optimisation, University of Waterloo, Waterloo, Ontario, Canada
We present a simple result on coloring hypergraphs and use it to obtain bounds on the chromatic number of graphs which do not induce certain trees. ## O. Introduction A class of graphs F is said to be x-bounded if there exists a functionfsuch that for all graphs G e F, (.) z(G) <~f(og(G)), where
Given a graph G, a total k-coloring of G is a simultaneous coloring of the vertices and edges of G with at most k colors. If β(G) is the maximum degree of G, then no graph has a total β-coloring, but Vizing conjectured that every graph has a total (β + 2)-coloring. This Total Coloring Conjecture rem