This note proves that the game chromatic number of an outerplanar graph is at most 7. This improves the previous known upper bound of the game chromatic number of outerplanar graphs.
Game chromatic index of k-degenerate graphs
β Scribed by Leizhen Cai; Xuding Zhu
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 147 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The strong chromatic index of a graph G, denoted sq(G), is the minimum number of parts needed to partition the edges of G into induced matchings. For 0 β€ k β€ l β€ m, the subset graph S m (k, l) is a bipartite graph whose vertices are the kand l-subsets of an m element ground set where two vertices ar
A k-critical (multi-) graph G has maximum degree k, chromatic index Ο (G) = k + 1, and Ο (G -e) < k + 1 for each edge e of G. For each k β₯ 3, we construct k-critical (multi-) graphs with certain properties to obtain counterexamples to some well-known conjectures.
We show that coloring the edges of a multigraph G in a particular order often leads to improved upper bounds for the chromatic index Ο (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 observe that the values of p for which with high probability Gm,p is k-colorable and for which with high probability G,,p has no k-core are not equal for k 2 4.