Clique Partitions of Glued Graphs
نویسنده
چکیده
A glued graph at K2-clone (K3-clone) results from combining two vertex-disjoint graphs by identifying an edge (a triangle) of each original graph. The clique covering numbers of these desired glued graphs have been investigated recently. Analogously, we obtain bounds of the clique partition numbers of glued graphs at K2-clones and K3-clones in terms of the clique partition numbers of their original graphs. Moreover, we characterize glued graphs satisfying such bounds.
منابع مشابه
Clique Coverings of Glued Graphs at Complete Clones
A clique covering of a graph G is a set of cliques of G in which each edge of G is contained in at least one clique. The smallest cardinality of clique coverings of G is called the clique covering number of G. A glued graph results from combining two nontrivial vertex-disjoint graphs by identifying nontrivial connected isomorphic subgraphs of both graphs. Such subgraphs are referred to as the c...
متن کاملPerfect Glued Graphs at Complete Clones
A graph G is called perfect if the chromatic number and the clique number have the same value for every of its induced subgraph. A glued graph results from combining two vertex-disjoint graphs by identifying connected isomorphic subgraphs of both graphs. Such subgraphs are referred to as the clones. We study the perfection of glued graphs whose clones are complete graphs. Our result generalizes...
متن کاملA characterisation of clique-width through nested partitions
Clique-width of graphs is defined algebraically through operations on graphs with vertex labels. We characterise the clique-width in a combinatorial way by means of partitions of the vertex set, using trees of nested partitions where partitions are ordered bottom-up by refinement. We show that the correspondences in both directions, between combinatorial partition trees and algebraic terms, pre...
متن کاملClique packings and clique partitions of graphs without odd chordles cycles
In this paper we consider partitions (resp. packings) of graphs without odd chordless cycles into cliques of order at least 2. We give a structure theorem, min-max results and characterization theorems for this kind of partitions and packings.
متن کاملCohen-Macaulay $r$-partite graphs with minimal clique cover
In this paper, we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is Cohen-Macaulay. It is proved that if there exists a cover of an $r$-partite Cohen-Macaulay graph by disjoint cliques of size $r$, then such a cover is unique.
متن کامل