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Mathematics OpenThe cycle graph of a graph G is the graph [Formula: see text] whose vertices are the induced cycles of G and where two vertices are adjacent if and only if they are distinct induced cycles that share a common edge.
Severino V. Gervacio, Yvette F. Lim
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New graph classes characterized by weak vertex separators and two-pairs
AKCE International Journal of Graphs and Combinatorics, 2017 A set of vertices whose deletion from a graph would increase the distance between two remaining vertices is called a weak vertex separator of the graph. Two vertices form a two-pair if all chordless paths between them have length .
Terry A. McKee
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A Zero Knowledge Authentication Protocol Based on Novel Heuristic Algorithm of Dense Induced Subgraphs Isomorphism [PDF]
Engineering and Technology Journal, 2015 Graphs provide an useful mathematical tool for modeling various real world phenomena. Dense graphs arise in many places of interest, for instance the internet and social networks to name just two. The density of a graph should be a real number reflecting
N. M. G. Al-Saidi +2 more
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Networks, EarlyView.ABSTRACT The minimum s$$ s $$‐t$$ t $$‐cut problem is one of the most‐studied problems in discrete optimization and has a unique complexity status in multi‐objective optimization. Even though the single‐objective version of the problem can be solved in polynomial time, it has been shown in the seminal work of Papadimitriou and Yannakakis (2000) that ...
Jan Boeckmann +4 more
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Strong ƒ-Star Factors of Graphs
Discussiones Mathematicae Graph Theory, 2015 Let G be a graph and f : V (G) → {2, 3, . . .}. A spanning subgraph F is called strong f-star of G if each component of F is a star whose center x satisfies degF (x) ≤ ƒ(x) and F is an induced subgraph of G.
Yan Zheng
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Solar RRL, EarlyView.This study investigates the effect of the chemical composition on the properties of A(BB’)(XX’)3$_3$ inorganic halide perovskites with density functional theory. By correlating distortion amplitudes with both composition and the Goldschmidt tolerance factor, we propose a pragmatic approach to designing more stable and efficient perovskites, advancing ...
Antoine Gissler +2 more
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List-3-Coloring ordered graphs with a forbidden induced subgraph [PDF]
, 2022 Sepehr Hajebi, Yanjia Li, Sophie Spirkl
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Methods in Ecology and Evolution, EarlyView.Abstract Quantifying the structure and dynamics of species interactions in ecological communities is fundamental to studying ecology and evolution. While there are numerous approaches to analysing ecological networks, there is not yet an approach that can (1) quantify dissimilarity in the global structure of ecological networks that range from ...
Kai M. Hung +4 more
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Chromatic number and regular subgraphs
Bulletin of the London Mathematical Society, EarlyView.Abstract In 1992, Erdős and Hajnal posed the following natural problem: Does there exist, for every r∈N$r\in \mathbb {N}$, an integer F(r)$F(r)$ such that every graph with chromatic number at least F(r)$F(r)$ contains r$r$ edge‐disjoint cycles on the same vertex set? We solve this problem in a strong form, by showing that there exist n$n$‐vertex graphs
Barnabás Janzer +2 more
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International Transactions in Operational Research, Volume 33, Issue 3, Page 1656-1677, May 2026.Abstract In graph‐restricted cooperative games, a group of agents, represented by the nodes of a graph, work together to make a profit. However, two agents can cooperate within a coalition only if they are connected by the graph in the coalition. Several allocation rules have been proposed for these games, but there is something in common in all of ...
Antonio C. Alarcón +2 more
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