Coloring graphs with stable cutsets
β Scribed by Alan Tucker
- Book ID
- 107884176
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 537 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We answer a question of Brandst adt et al. by showing that deciding whether a line graph with maximum degree 5 has a stable cutset is NP-complete. Conversely, the existence of a stable cutset in a line graph with maximum degree at most 4 can be decided e ciently. The proof of our NP-completeness res
Cliques and odd cycles are well known to induce facet-deΓΏning inequalities for the stable set polytope. In graph coloring cliques are a class of n-critical graphs whereas odd cycles represent the class of 3-critical graphs. In the ΓΏrst part of this paper we generalize both notions to (Kn \ e)-cycles
It is shown that the chromatic number of any graph with maximum degree d in which the number of edges in the induced subgraph on the set of all neighbors of any vertex does not exceed d 2 Γf is at most O(dΓlog f ). This is tight (up to a constant factor) for all admissible values of d and f.
We consider graphs that have a clique-cutset, and we show that this property preserves the existence of a kernel in a certain sense. We consider finite directed graphs that do not have multiple arcs or loops, but there may be symmetric arcs between some pairs of vertices. Let G = (V, A) be a direct