A graph coloring algorithm that immediately colors the vertices taken from a list without looking ahead or changing colors already assigned is called "on-line coloring." The properties of on-line colorings are investigated in several classes of graphs. In many cases w e find on-line colorings that u
Coloring interval graphs with first-fit
β Scribed by H.A. Kierstead; Jun Qin
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 569 KB
- Volume
- 144
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Improved bounds on the performance of the on-line graph coloring algorithm First-Fit on interval graphs are obtained.
π SIMILAR VOLUMES
## This paper is complementary to Kubale (1989). We consider herein a problem of interval coloring the edges of a graph under the restriction that certain colors cannot be used for some edges. We give lower and upper bounds on the minimum number of colors required for such a coloring. Since the ge
An edge-coloring of a simple graph \(G\) with colors \(1,2, \ldots, t\) is called an interval \(t\)-coloring [3] if at least one edge of \(G\) is colored by color \(i, i=1, \ldots, t\) and the edges incident with each vertex \(x\) are colored by \(d_{G}(x)\) consecutive colors, where \(d_{G}(x)\) is
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.
## Abstract An interval coloring of a graph is a proper edge coloring such that the set of used colors at every vertex is an interval of integers. Generally, it is an NPβhard problem to decide whether a graph has an interval coloring or not. A bipartite graph __G__β=β(__A__,__B__;__E__) is (Ξ±, Ξ²)βb