A Combined Logarithmic Bound on the Chromatic Index of Multigraphs
โ Scribed by Michael Plantholt*
- Book ID
- 112121132
- Publisher
- John Wiley and Sons
- Year
- 2012
- Tongue
- English
- Weight
- 630 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We show that coloring the edges of a multigraph G in a particular order often leads to improved upper bounds for the chromatic index ฯ (G). Applying this to simple graphs, we significantly generalize recent conditions based on the core of G (i.e., the subgraph of G induced by the vertices of degree
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
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