By applying a sequence of edge-gluings on a set of cycles each of length k, we obtain a special series-parallel graph. The well-known k-gon tree theorem (see [l, lo]) states that these graphs form a X-equivalence class. Many of the other known classes of X-unique graphs and X-equivalence classes are
The Entire Coloring of Series-Parallel Graphs
โ Scribed by Jian-liang Wu; Yu-liang Wu
- Publisher
- Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2005
- Tongue
- English
- Weight
- 246 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0168-9673
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In 1973, Kronk and Mitchem (Discrete Math. (5) 255-260) conjectured that the vertices, edges and faces of each plane graph G may be colored with D(G) + 4 colors, where D(G) is the maximum degree of G, so that any two adjacent or incident elements receive distinct colors. They succeeded in verifying
In this article, we consider the circular chromatic number ฯ c (G) of series-parallel graphs G. It is well known that series-parallel graphs have chromatic number at most 3. Hence, their circular chromatic numbers are at most 3. If a seriesparallel graph G contains a triangle, then both the chromati
## Abstract A __k__โfold coloring of a graph is a function that assigns to each vertex a set of __k__ colors, so that the color sets assigned to adjacent vertices are disjoint. The __k__th chromatic number of a graph __G__, denoted by ฯ~__k__~(__G__), is the minimum total number of colors used in a