Bounded color functions on graphs
β Scribed by D. W. Matula
- Publisher
- John Wiley and Sons
- Year
- 1972
- Tongue
- English
- Weight
- 753 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The purpose of this note is to point out a relationship between graph coloring and monotone functions defined on posets. This relationship permits us to deduce certain properties of the chromatic polynomial of a graph.
## Abstract A __polychromatic k__β__coloring__ of a plane graph __G__ is an assignment of __k__ colors to the vertices of __G__ such that every face of __G__ has __all k__ colors on its boundary. For a given plane graph __G__, one seeks the __maximum__ number __k__ such that __G__ admits a polychro
It is shown that there is a constant \(c\) such that if \(G\) is a graph embedded in a surface of genus \(g\) (either orientable or non-orientable) and the length of a shortest non-bounding cycle of \(G\) is at least \(c \log (g+1)\), then \(G\) is six-colorable. A similar result holds for three- an
## Abstract A graph __G__ is degreeβboundedβcolorable (briefly, dbβcolorable) if it can be properly vertexβcolored with colors 1,2, β¦, k β€ Ξ(__G__) such that each vertex __v__ is assigned a color __c__(__v__) β€ __v__. We first prove that if a connected graph __G__ has a block which is neither a com
For a graph H , the H-coloring problem is to decide whether or not an instance graph G is homomorphic to H . The H-coloring problem is said to have bounded treewidth duality if there is an integer k such that for any graph G which is not homomorphic to H , there is a graph F of treewidth k which is