منابع مشابه
Simple Reduction of f-Colorings to Edge-Colorings
Abs t r ac t . In an edge-coloring of a graph G = (V, E) each color appears around each vertex at most once. An f-coloring is a generalization of an edge-coloring in which each color appears around each vertex v at most f(v) times where f is a function assigning a natural number f(v) e N to each vertex v E V. In this paper we first give a simple reduction of the f-coloring problem to the ordina...
متن کاملOn local colorings of Cartesian product graphs
A local coloring of a graph G is a function c : V (G) → N such that for each S ⊆ V (G), 2 ≤ |S| ≤ 3, there exist u, v ∈ S with |c(u) − c(v)| at least the size of the subgraph induced by S. The maximum color assigned by c is the value χl(c) of c, and the local chromatic number of G is χl(G) = min{χl(c) : c local coloring of G}. In this note the local chromatic number is determined for Cartesian ...
متن کاملNonrepetitive colorings of lexicographic product of graphs
A coloring c of the vertices of a graph G is nonrepetitive if there exists no path v1v2 . . . v2l for which c(vi) = c(vl+i) for all 1 ≤ i ≤ l. Given graphs G and H with |V (H)| = k, the lexicographic product G[H ] is the graph obtained by substituting every vertex of G by a copy of H , and every edge of G by a copy of Kk,k. We prove that for a sufficiently long path P , a nonrepetitive coloring...
متن کاملEquitable colorings of non-uniform simple hypergraphs
The paper is devoted to the combinatorial problem concerning equitable colorings of non-uniform simple hypergraphs. Let H = (V,E) be a hypergraph, a coloring with r colors of its vertex set V is called equitable if it is proper (i.e. none of the edges is monochromatic) and the cardinalities of the color classes differ by at most one. We show that if H is a simple hypergraph with minimum edge-ca...
متن کاملWeak Conflict-Free Colorings of Point Sets and Simple Regions
In this paper we consider the weak conflict-free colorings of regions and points. This is a natural relaxation of conflict-free coloring [ELRS03]. One of the most interesting type of regions to consider for this problem is that of the axis-parallel rectangles. We completely solve the problem for a special case of them, for bottomless rectangles. We also give complete answer for half-planes and ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1984
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90133-x