منابع مشابه
Strong total chromatic numbers of complete hypergraphs
We determine the strong total chromatic number of the complete h-uniform hypergraph Kh, and the complete h-partite hypergraph K,
متن کاملOn the set of circular total chromatic numbers of graphs
For every integer r > 3 and every ε > 0 we construct a graph with maximum degree r − 1 whose circular total chromatic number is in the interval (r, r + ε). This proves that (i) every integer r > 3 is an accumulation point of the set of circular total chromatic numbers of graphs, and (ii) for every ∆ > 2, the set of circular total chromatic numbers of graphs with maximum degree ∆ is infinite. Al...
متن کاملMixed Ramsey numbers: total chromatic number versus stars
Guantao Chen Department of Mathematics and Computing Science Georgia State University ATLANTA GA 30303 USA Given a graph theoretic parameter f, a graph H and a positive integer m, the mixed ramsey number f(m,H) is defmed as the least positive integer p such that for any graph G of order p either f(G) ~ m or G contains H as a subgraph. In this paper we determine the mixed ramsey number X2(m,K( I...
متن کاملThe total chromatic numbers of joins of sparse graphs
In this paper, we investigate the total colorings of the join graphs G = G1+G2, where G1 and G2 are graphs with maximum degree at most two. We prove that (1) when both G1 and G2 are bipartite graphs with maximum degree at most two, then G is Type 1 if and only if G is not isomorphic to Kn,n (n = 1, 2, . . .) or to K4, and (2) Cm + Cn is Type 2 if and only if m = n and n is odd. ∗ This research ...
متن کاملGraphs with Tiny Vector Chromatic Numbers and Huge Chromatic Numbers
Karger, Motwani and Sudan (JACM 1998) introduced the notion of a vector coloring of a graph. In particular they show that every k-colorable graph is also vector kcolorable, and that for constant k, graphs that are vector kcolorable can be colored by roughly 1 2=k colors. Here is the maximum degree in the graph. Their results play a major role in the best approximation algorithms for coloring an...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1992
ISSN: 0893-9659
DOI: 10.1016/0893-9659(92)90010-7