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Graphs with Strong Proper Connection Numbers and Large Cliques
Axioms, 2023 In this paper, we mainly investigate graphs with a small (strong) proper connection number and a large clique number. First, we discuss the (strong) proper connection number of a graph G of order n and ω(G)=n−i for 1⩽i⩽3. Next, we investigate the rainbow
Yingbin Ma, Xiaoxue Zhang, Yanfeng Xue
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S2-HGNN: Scale-Aware Hypergraph Node Classification with Spectral Inductive Bias [PDF]
EntropyExisting methods for hypergraph node classification usually rely on local message passing and use a unified strategy for topological modeling across hyperedges of different sizes. However, they have two limitations in semi-supervised settings.
Jiangnan Zhou +7 more
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Fast Diameter Computation within Split Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 When can we compute the diameter of a graph in quasi linear time? We address this question for the class of {\em split graphs}, that we observe to be the hardest instances for deciding whether the diameter is at most two.
Guillaume Ducoffe +2 more
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Strong Cliques in Claw-Free Graphs [PDF]
Graphs and Combinatorics, 2021 AbstractFor a graph G, $$L(G)^2$$ L ( G ) 2 is the square of the line graph of G – that is ...
Michal Debski +1 more
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Strong Cliques in Diamond-Free Graphs [PDF]
Theoretical Computer Science, 2020 An extended abstract of this work was accepted at WG ...
Nina Chiarelli +4 more
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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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Graphs vertex-partitionable into strong cliques [PDF]
Discrete Mathematics, 2018 A graph is said to be well-covered if all its maximal independent sets are of the same size. In 1999, Yamashita and Kameda introduced a subclass of well-covered graphs, called localizable graphs and defined as graphs having a partition of the vertex set into strong cliques, where a clique in a graph is strong if it intersects all maximal independent ...
Ademir Hujdurovic +2 more
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Beyond Topological Persistence: Starting from Networks
Mathematics, 2021 Persistent homology enables fast and computable comparison of topological objects. We give some instances of a recent extension of the theory of persistence, guaranteeing robustness and computability for relevant data types, like simple graphs and ...
Mattia G. Bergomi +3 more
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Finding a Strong Stable Set or a Meyniel Obstruction in any Graph [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 A strong stable set in a graph $G$ is a stable set that contains a vertex of every maximal clique of $G$. A Meyniel obstruction is an odd circuit with at least five vertices and at most one chord.
Kathie Cameron, Jack Edmonds
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Detecting strong cliques [PDF]
Discrete Mathematics, 2019 A strong clique in a graph is a clique intersecting every maximal independent set. We study the computational complexity of six algorithmic decision problems related to strong cliques in graphs and almost completely determine their complexity in the classes of chordal graphs, weakly chordal graphs, line graphs and their complements, and graphs of ...
Ademir Hujdurovic +2 more
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