Suppose /(G)=r and P V(G). It is known that if the distance between any two vertices in P is at least 4, then any (r+1)-coloring of P extends to an (r+1)-coloring of all of G, but an r-coloring of P might not extend to an r-coloring of G. We show that if the distance between any two vertices in P is
Weighted-Set Graph Colorings
β Scribed by Robert Shrock; Yan Xu
- Publisher
- Springer
- Year
- 2010
- Tongue
- English
- Weight
- 767 KB
- Volume
- 139
- Category
- Article
- ISSN
- 0022-4715
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π SIMILAR VOLUMES
Suppose that G is a finite simple graph and w is a weight function which assigns to each vertex of G a nonnegative real number. Let C be a circle of length t . A t-circular coloring of (G,w) is a mapping A of the vertices of G to arcs of C such that A(%) n A(y) = 0 if (x, y) E E ( G ) and A(x) has l
Given a property P, graph G. and k 2 0, a P k-coloring is a function 7r: V(G) + { I , ... , k) such that the subgraph induced by each color class has property P; x ( G : P ) is the least k, for which G has a P k-coloring. We investigate here the theory of P colorings. Generalizations of the wellknow
## Abstract The notion of (circular) colorings of edgeβweighted graphs is introduced. This notion generalizes the notion of (circular) colorings of graphs, the channel assignment problem, and several other optimization problems. For instance, its restriction to colorings of weighted complete graphs