Add to ORKGLet G[H] be the lexicographic product of graphs G and H and let G⊕H be their Cartesian sum. It is proved that if G is a nonbipartite graph, then for any graph H, χ(G[H]) ≥ 2χ(H)+dχ(H)k e, where 2k+1 is the length of a shortest odd cycle of G. Chromatic numbers of the Cartesian sum of graphs are also considered. It is shown in particular that for χ–critical and not complete graphs G and H, χ(G ⊕ H) ≤ χ(G)χ(H)−1. These bounds are used to calculate chromatic numbers of the Cartesian sum of two odd cycles. Finally, a connection of some colorings with hypergraphs is given.
Abstract. The game chromatic number χg is considered for the Cartesian product G2H of two graphs G a...
AbstractIt is shown that the difference between the chromatic number χ and the fractional chromatic ...
The circular chromatic index of a graph G, written χ′c(G), is the minimum r per-mitting a function f...
AbstractLet G[H] be the lexicographic product of graphs G and H and let G ⊕ H be their Cartesian sum...
AbstractFor graphs G and H, let G⊕H denote their Cartesian sum. We investigate the chromatic number ...
For graphs G and H, let G ⊕ H denote their Cartesian sum. We investigate the chromatic number and th...
AbstractThe chromatic difference sequence cds(G) of a graph G with chromatic number n is defined by ...
AbstractFor graphs G and H let G[H] be their lexicographic product and let χƒ(G) = inf{χ(G[Kn])/n | ...
For graphs G and H let G[H] be their lexicographic product and let χf (G) = inf{χ(G[Kn])/n | n = 1, ...
AbstractThe square G2 of a graph G is defined on the vertex set of G in such a way that distinct ver...
For the lexicographic product $G\bullet H$ of two graphs $G$ and $H$ so that $G$ is connected, we pr...
An upper bound for the chromatic number of the lexicographic product of graphs which unifies and gen...
A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two verti...
The square G2 of a graph G is defined on the vertex set of G in such a way that distinct vertices wi...
AbstractA well-established generalization of graph coloring is the concept of list coloring. In this...
Abstract. The game chromatic number χg is considered for the Cartesian product G2H of two graphs G a...
AbstractIt is shown that the difference between the chromatic number χ and the fractional chromatic ...
The circular chromatic index of a graph G, written χ′c(G), is the minimum r per-mitting a function f...
AbstractLet G[H] be the lexicographic product of graphs G and H and let G ⊕ H be their Cartesian sum...
AbstractFor graphs G and H, let G⊕H denote their Cartesian sum. We investigate the chromatic number ...
For graphs G and H, let G ⊕ H denote their Cartesian sum. We investigate the chromatic number and th...
AbstractThe chromatic difference sequence cds(G) of a graph G with chromatic number n is defined by ...
AbstractFor graphs G and H let G[H] be their lexicographic product and let χƒ(G) = inf{χ(G[Kn])/n | ...
For graphs G and H let G[H] be their lexicographic product and let χf (G) = inf{χ(G[Kn])/n | n = 1, ...
AbstractThe square G2 of a graph G is defined on the vertex set of G in such a way that distinct ver...
For the lexicographic product $G\bullet H$ of two graphs $G$ and $H$ so that $G$ is connected, we pr...
An upper bound for the chromatic number of the lexicographic product of graphs which unifies and gen...
A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two verti...
The square G2 of a graph G is defined on the vertex set of G in such a way that distinct vertices wi...
AbstractA well-established generalization of graph coloring is the concept of list coloring. In this...
Abstract. The game chromatic number χg is considered for the Cartesian product G2H of two graphs G a...
AbstractIt is shown that the difference between the chromatic number χ and the fractional chromatic ...
The circular chromatic index of a graph G, written χ′c(G), is the minimum r per-mitting a function f...