Results 1 to 10 of about 8,623,913 (295)
Tight Bounds on the Clique Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2021 The clique chromatic number of a graph is the minimum number of colours needed to colour its vertices so that no inclusion-wise maximal clique which is not an isolated vertex is monochromatic. We show that every graph of maximum degree $\Delta$ has clique chromatic number $O\left(\frac{\Delta}{\log~\Delta}\right)$.
Joret, Gwenaël +3 more
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Clique number of tournaments [PDF]
CoRR, 2023 Given a digraph $D$ together with an ordering $\prec$ of its vertices, the \emph{backedge graph} of $D$ with respect to $\prec$ is the undirected graph $D^{\prec}$ with the same vertex set as $D$, where $xy \in E(D^{\prec})$ if $xy \in A(D)$ and $y \prec x$.
Pierre Aboulker +3 more
core +4 more sources
Squares of Low Clique Number [PDF]
Electronic Notes in Discrete Mathematics, 2016 The Square Root problem is that of deciding whether a given graph admits a square root. This problem is only known to be NP-complete for chordal graphs and polynomial-time solvable for non-trivial minor-closed graph classes and a very limited number of other graph classes.
Petr A. Golovach +3 more
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Clique immersions and independence number [PDF]
European Journal of Combinatorics, 2022 13 pages, 1 figure.
Sebastián Bustamante 0001 +3 more
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The Smallest Spectral Radius of Graphs with a Given Clique Number [PDF]
The Scientific World Journal, 2014 The first four smallest values of the spectral radius among all connected graphs with maximum clique size ω≥2 are obtained.
Jing-Ming Zhang +2 more
doaj +2 more sources
On clique‐inverse graphs of graphs with bounded clique number [PDF]
Journal of Graph Theory, 2020 AbstractThe clique graph K(G) of G is the intersection graph of the family of maximal cliques of G. For a family of graphs, the family of clique‐inverse graphs of , denoted by , is defined as . Let be the family of Kp‐free graphs, that is, graphs with clique number at most p − 1, for an integer constant p ≥ 2.
Liliana Alcón +4 more
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A local core number based algorithm for the maximum clique problem [PDF]
Transactions on Combinatorics, 2021 The maximum clique problem (MCP) is to determine a complete subgraph of maximum cardinality in a graph. MCP is a fundamental problem in combinatorial optimization and is noticeable for its wide range of applications.
Neda Mohammadi, Mehdi Kadivar
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Exact square coloring of graphs resulting from some graph operations and products
AKCE International Journal of Graphs and Combinatorics, 2022 A vertex coloring of a graph [Formula: see text] is called an exact square coloring of G if any pair of vertices at distance 2 receive distinct colors.
Priyamvada, B. S. Panda
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Some Extremal Graphs with Respect to Sombor Index
Mathematics, 2021 Let G be a graph with set of vertices V(G)(|V(G)|=n) and edge set E(G). Very recently, a new degree-based molecular structure descriptor, called Sombor index is denoted by SO(G) and is defined as SO=SO(G)=∑vivj∈E(G)dG(vi)2+dG(vj)2, where dG(vi) is the ...
Kinkar Chandra Das, Yilun Shang
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Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph [PDF]
Neutrosophic Sets and Systems, 2022 New setting is introduced to study dominating, resolving, coloring, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophicnumber, independent number, independent neutrosophic ...
Henry Garrett
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