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Inverse Clique Domination in Graphs
Recoletos Multidisciplinary Research Journal, 2016 Let G be a connected simple graph. A nonempty subset S of the vertex set V (G) is a clique in G if the graph induced by S is complete. A clique S in G is a clique dominating set if it is a dominating set.
Carmelita Loquias +2 more
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Cliques in rank-1 random graphs: the role of inhomogeneity [PDF]
, 2019 We study the asymptotic behavior of the clique number in rank-1 inhomogeneous random graphs, where edge probabilities between vertices are roughly proportional to the product of their vertex weights.
Bogerd, Kay +2 more
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Triangle-free intersection graphs of line segments with large chromatic number [PDF]
, 2012 In the 1970s, Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no.
Arkadiusz Pawlik +20 more
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Local and Global Clique Numbers
Journal of Combinatorial Theory, Series B, 1994 A graph \(G\) is said to have the \((p,q)\)-property for some integers \(p\geq q\geq 2\) if for every \(p\)-set of its vertices the induced subgraph contains a \(q\)-clique. The aim of the paper is to investigate relations of the type \((p,q)\to (n,s)\), meaning that each graph having the \((p,q)\)- property also has the \((n,s)\)-property.
Linial, N., Rabinovich, Y.
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Clique descriptor of affine invariant regions for robust wide baseline image matching [PDF]
, 2010 Assuming that the image distortion between corresponding regions of a stereo pair of images with wide baseline can be approximated as an affine transformation if the regions are reasonably small, recent image matching algorithms have focused on affine ...
Shin, Dongjoe, Tjahjadi, Tardi
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Minimum Clique Number, Chromatic Number, and Ramsey Numbers [PDF]
The Electronic Journal of Combinatorics, 2012 Let $Q(n,c)$ denote the minimum clique number over graphs with $n$ vertices and chromatic number $c$. We investigate the asymptotics of $Q(n,c)$ when $n/c$ is held constant. We show that when $n/c$ is an integer $\alpha$, $Q(n,c)$ has the same growth order as the inverse function of the Ramsey number $R(\alpha+1,t)$ (as a function of $t$). Furthermore,
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Connected Domination Number and a New Invariant in Graphs with Independence Number Three [PDF]
Computer Science Journal of Moldova, 2021 Adding a connected dominating set of vertices to a graph $G$ increases its number of Hadwiger $h(G)$. Based on this obvious property in [2] we introduced a new invariant $\eta(G)$ for which $\eta(G)\leq h(G)$. We continue to study its property.
Vladimir Bercov
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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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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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Discrete Mathematics, 1986 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Erdös, Paul, Erné, Marcel
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