Results 11 to 20 of about 80,797 (168)
Improved Algorithms for Recognizing Perfect Graphs and Finding Shortest Odd and Even Holes [PDF]
arXiv.org, 2022 An induced subgraph of an n -vertex graph G is a graph that can be obtained by deleting a set of vertices together with its incident edges from G . A hole of G is an induced cycle of G with length at least four. A hole is odd (respectively, even ) if its
Yung-Chung Chiu +2 more
semanticscholar +1 more source
Strong and Weak Perfect Digraph Theorems for Perfect, α-Perfect and Strictly Perfect Digraphs
Discussiones Mathematicae Graph Theory, 2021 Perfect digraphs have been introduced in [S.D. Andres and W. Hochstättler, Perfect digraphs, J. Graph Theory 79 (2015) 21–29] as those digraphs where, for any induced subdigraph, the dichromatic number and the symmetric clique number are equal.
S. Andres
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Forbidden Induced Pairs for Perfectness and $\omega$-Colourability of Graphs [PDF]
Electronic Journal of Combinatorics, 2021 We characterise the pairs of graphs $\{ X, Y \}$ such that all $\{ X, Y \}$-free graphs (distinct from $C_5$) are perfect. Similarly, we characterise pairs $\{ X, Y \}$ such that all $\{ X, Y \}$-free graphs (distinct from $C_5$) are $\omega$-colourable (
M. Chudnovsky +3 more
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A constructive formalization of the weak perfect graph theorem [PDF]
Certified Programs and Proofs, 2019 The Perfect Graph Theorems are important results in graph theory describing the relationship between clique number ω(G) and chromatic number χ(G) of a graph G. A graph G is called perfect if χ(H)=ω(H) for every induced subgraph H of G. The Strong Perfect
Abhishek Kr Singh, R. Natarajan
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Graphs of bounded cliquewidth are polynomially χ-bounded
arXiv.org, 2020 A trivial lower bound on the chromatic number of a graph is its clique number. In general, there is no upper bound on the chromatic number as a function of its clique number.
Marthe Bonamy, Michał Pilipczuk
semanticscholar +1 more source
Counting Homomorphisms to Square-Free Graphs, Modulo 2 [PDF]
TOCT, 2015 We study the problem ⊕HomsToH of counting, modulo 2, the homomorphisms from an input graph to a fixed undirected graph H. A characteristic feature of modular counting is that cancellations make wider classes of instances tractable than is the case for ...
Andreas Göbel +2 more
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Combinatorial secant varieties [PDF]
, 2005 The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a ...
B. Sturmfels, S. Sullivant
semanticscholar +1 more source
Local Search and the Evolution of World Models
Topics in Cognitive Science, EarlyView., 2023 Abstract An open question regarding how people develop their models of the world is how new candidates are generated for consideration out of infinitely many possibilities. We discuss the role that evolutionary mechanisms play in this process. Specifically, we argue that when it comes to developing a global world model, innovation is necessarily ...
Neil R. Bramley +3 more
wiley +1 more source
An Introduction to Predictive Processing Models of Perception and Decision‐Making
Topics in Cognitive Science, EarlyView., 2023 Abstract The predictive processing framework includes a broad set of ideas, which might be articulated and developed in a variety of ways, concerning how the brain may leverage predictive models when implementing perception, cognition, decision‐making, and motor control.
Mark Sprevak, Ryan Smith
wiley +1 more source
Computational Modeling of Reticular Materials: The Past, the Present, and the Future
Advanced Materials, EarlyView.Reticular materials are advanced materials with applications in emerging technologies. A thorough understanding of material properties at operating conditions is critical to accelerate the deployment at an industrial scale. Herein, the status of computational modeling of reticular materials is reviewed, supplemented with topical examples highlighting ...
Wim Temmerman +3 more
wiley +1 more source