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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TL;DR: The structure of an unoriented graph R d on the set of reflexive polytopes of a fixed dimension d is suggested, and an explicit finite list of quivers is presented giving all d -dimensional reflexive flow poly topes up to lattice isomorphism.
8 citations
TL;DR: A uniform cut polytope is defined as the convex hull of the incidence vectors of all cuts in an undirected graph G for which the cardinalities of the shores are fixed and linear descriptions are studied.
8 citations
TL;DR: In this paper, the authors formulate a continuous characterization of the maximum clique problem based on the symmetric rank-one nonnegative approximation of a given matrix, and build a one-to-one correspondence between stationary points of their formulation and cliques of the given graph.
Abstract: Finding complete subgraphs in a graph, that is, cliques, is a key problem and has many real-world applications, e.g., finding communities in social networks, clustering gene expression data, modeling ecological niches in food webs, and describing chemicals in a substance. The problem of finding the largest clique in a graph is a well-known NP-hard problem and is called the maximum clique problem (MCP). In this paper, we formulate a very convenient continuous characterization of the MCP based on the symmetric rank-one nonnegative approximation of a given matrix, and build a one-to-one correspondence between stationary points of our formulation and cliques of a given graph. In particular, we show that the local (resp. global) minima of the continuous problem corresponds to the maximal (resp. maximum) cliques of the given graph. We also propose a new and efficient clique finding algorithm based on our continuous formulation and test it on various synthetic and real data sets to show that the new algorithm outperforms other existing algorithms based on the Motzkin-Straus formulation, and can compete with a sophisticated combinatorial heuristic.
8 citations
8 citations
TL;DR: By generalizing the idea of extended triangle of a graph, a common framework is obtained for the result of Roberts and Spencer about clique graphs and the one of Szwarcfiter about Helly graphs is obtained.
8 citations