Topic
K-tree
About: K-tree is a research topic. Over the lifetime, 427 publications have been published within this topic receiving 12096 citations.
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01 Jan 2010
TL;DR: In this paper, the clique covering number of a graph G is defined as the set of cliques of G in which each edge of G is contained in at least one clique.
Abstract: 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 clones. The two nontrivial vertexdisjoint graphs are referred to the original graphs. In this paper, we investigate bounds of clique covering numbers of glued graphs at clone which is isomorphic to Kn in terms of clique covering numbers of their original graphs, and give a characterization of a glued graph with the clique covering number of each possible value.
3 citations
22 May 2017
TL;DR: A formal concept analysis based approach for detecting the bases of maximal cliques and detection theorem is proposed and it is believed that this work can provide a new research solution and direction for future topological structure analysis in various complex networking systems.
Abstract: Maximal Cliques Enumeration (MCE), as a fundamental problem, has been extensively investigated in many fields, such as social networks, and biological science and so forth. However, the existing research works usually ignore the formation principle of maximal cliques which can help us to speed up the detection of maximal cliques in a graph. This paper pioneers a novel problem on detection of bases of maximal cliques in a graph. We propose a formal concept analysis based approach for detecting the bases of maximal cliques and detection theorem. It is believed that our work can provide a new research solution and direction for future topological structure analysis in various complex networking systems.
3 citations
TL;DR: A general scheme for constructing polytopes is implemented in this article specifically for the classes of the most important 3D polytes, namely those whose vertices are labeled by integers relative to a particular basis, here called the ω-basis.
Abstract: A general scheme for constructing polytopes is implemented here specifically for the classes of the most important 3D polytopes, namely those whose vertices are labeled by integers relative to a particular basis, here called the ω-basis. The actual number of non-isomorphic polytopes of the same group has no limit. To put practical bounds on the number of polytopes to consider for each group we limit our consideration to polytopes with dominant point (vertex) that contains only nonnegative integers in ω-basis. A natural place to start the consideration of polytopes from is the generic dominant weight which were all three coordinates are the lowest positive integer numbers. Contraction is a continuous change of one or several coordinates to zero.
3 citations
TL;DR: A representation for chordal graphs called the compact representation, based on the running intersection property, is presented, which provides the means to immediately deduce several structural properties of a chordal graph such as a perfect elimination ordering, the minimal vertex separators and a clique-tree.
3 citations