Results 51 to 60 of about 47,591 (350)
On a class of polynomials associated with the Cliques in a graph and its applications
International Journal of Mathematics and Mathematical Sciences, 1989 The clique polynomial of a graph is defined. An explicit formula is then derived for the clique polynomial of the complete graph. A fundamental theorem and a reduction process is then given for clique polynomials.
E. J. Farrell
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Hard optimization problems have soft edges
Scientific Reports, 2023 Finding a Maximum Clique is a classic property test from graph theory; find any one of the largest complete subgraphs in an Erdös-Rényi G(N, p) random graph. We use Maximum Clique to explore the structure of the problem as a function of N, the graph size,
Raffaele Marino, Scott Kirkpatrick
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CoRRIn the $K_r$-Cover problem, given a graph $G$ and an integer $k$ one has to decide if there exists a set of at most $k$ vertices whose removal destroys all $r$-cliques of $G$. In this paper we give an algorithm for $K_r$-Cover that runs in subexponential FPT time on graph classes satisfying two simple conditions related to cliques and treewidth.
Berthe, Gaétan +3 more
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A New Implicit Branching Strategy for Exact Maximum Clique
, 2010 We present a new implicit branching strategy for maximum clique. The new strategy is based in Konj and Janečič's improvement over reference MCR algorithm.
Tapia García, Cristóbal +3 more
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High Density Subspace Clustering Algorithm for High Dimensional Data
Journal of Harbin University of Science and Technology, 2020 Highdimensional data have the characteristics of sparsity and vulnerability to dimension disaster, which makes it is difficult to ensure the precision and efficiency of high dimensional data clustering Therefore the method of subspace clustering is ...
WAN Jing +3 more
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On clique graphs and clique regular graphs
Discrete MathematicsIf $Γ$ is a graph for which every edge is in exactly one clique of order $ω$, then one can form a new graph with vertex set equal to these cliques. This is a generalization of the line graph of $Γ$. We discover many general results and classifications related to these clique graph that will be useful to researchers studying these objects. In particular,
Robert R. Petro, Connor M. Phillips
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Between clique-width and linear clique-width of bipartite graphs [PDF]
, 2020 We consider hereditary classes of bipartite graphs where clique-width is bounded, but linear clique-width is not. Our goal is identifying classes that are critical with respect to linear clique-width.
Lozin, V +8 more
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SIAM Journal on Discrete MathematicsWe study how many copies of a graph $F$ that another graph $G$ with a given number of cliques is guaranteed to have. For example, one of our main results states that for all $t\ge 2$, if $G$ is an $n$ vertex graph with $kn^{3/2}$ triangles and $k$ is sufficiently large in terms of $t$, then $G$ contains at least \[Ω(\min\{k^t n^{3/2},k^{\frac{2t^2}{3t-
Quentin Dubroff +3 more
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shah314/clique: Genetic Algorithm for the Maximum Clique Problem
, 2019 <p>Implementation of a genetic algorithm for the maximum clique problem in C++. A clique of a graph is a set of vertices in which each pair in the set have an edge between them i.e. it is a complete subgraph.
Shalin Shah
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Electronic Notes in Discrete Mathematics, 2017 Abstract Basic definitions are given in the next paragraph. We study second clique graphs of suspensions of graphs, K 2 ( S ( G ) ) , and characterize them, in terms of an auxiliary biclique operator B which transforms a graph G into its biclique graph B(G). The characterization is then: K 2 ( S ( G ) ) ≅ B ( K (
Miguel A. Pizaña, I. A. Robles
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