On chromatic and achromatic numbers of uniform hypergraphs
On chromatic number of product of graphs
On chromatic number of products of two graphs
On chromatic uniqueness of a family of -homeomorphs.
On chromaticity of graphs
In this paper we obtain the explicit formulas for chromatic polynomials of cacti. From the results relating to cacti we deduce the analogous formulas for the chromatic polynomials of n-gon-trees. Besides, we characterize unicyclic graphs by their chromatic polynomials. We also show that the so-called clique-forest-like graphs are chromatically equivalent.
On Closed Modular Colorings of Trees
Two vertices u and v in a nontrivial connected graph G are twins if u and v have the same neighbors in V (G) − {u, v}. If u and v are adjacent, they are referred to as true twins; while if u and v are nonadjacent, they are false twins. For a positive integer k, let c : V (G) → Zk be a vertex coloring where adjacent vertices may be assigned the same color. The coloring c induces another vertex coloring c′ : V (G) → Zk defined by c′(v) = P u∈N[v] c(u) for each v ∈ V (G), where N[v] is the closed neighborhood...
On co-bicliques
A co-biclique of a simple undirected graph G = (V,E) is the edge-set of two disjoint complete subgraphs of G. (A co-biclique is the complement of a biclique.) A subset F ⊆ E is an independent of G if there is a co-biclique B such that F ⊆ B, otherwise F is a dependent of G. This paper describes the minimal dependents of G. (A minimal dependent is a dependent C such that any proper subset of C is an independent.) It is showed that a minimum-cost dependent set of G can be determined in polynomial...
On coloring the odd-distance graph.
On colorings avoiding a rainbow cycle and a fixed monochromatic subgraph.
On colouring products of graphs
In this paper, we give some results concerning the colouring of the product (cartesian product) of two graphs.
On detectable colorings of graphs
Let be a connected graph of order and let be a coloring of the edges of (where adjacent edges may be colored the same). For each vertex of , the color code of with respect to is the -tuple , where is the number of edges incident with that are colored (). The coloring is detectable if distinct vertices have distinct color codes. The detection number of is the minimum positive integer for which has a detectable -coloring. We establish a formula for the detection...
On distance edge colourings of a cyclic multigraph
On distance local connectivity and vertex distance colouring
In this paper, we give some sufficient conditions for distance local connectivity of a graph, and a degree condition for local connectivity of a k-connected graph with large diameter. We study some relationships between t-distance chromatic number and distance local connectivity of a graph and give an upper bound on the t-distance chromatic number of a k-connected graph with diameter d.
On distinguishing and distinguishing chromatic numbers of hypercubes
The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d colors that is not preserved by any nontrivial automorphism. The restriction to proper labelings leads to the definition of the distinguishing chromatic number of G. Extending these concepts to infinite graphs we prove that and , where denotes the hypercube of countable dimension. We also show that , thereby completing the investigation of finite hypercubes with respect to . Our results...
On edge colorings with at least colors in every subset of vertices.
On edge domatic number of hypercubes
On edge-colorings of graphs.
On -edge cover coloring of nearly bipartite graphs.
On feasible sets of mixed hypergraphs.
On four-colourings of the rational four-space.