Results 81 to 90 of about 1,168 (127)
Cograph generation with linear delay [PDF]
Theoretical Computer Science, 2018 Cographs have always been a research target in areas such as coloring, graph decomposition, and spectral theory. In this work, we present an algorithm to generate all unlabeled cographs with $n$ vertices, based on the generation of cotrees. The delay of our algorithm (time spent between two consecutive outputs) is $O(n)$.
Jones, Átila A. +2 more
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Combinatorial Hopf algebraic description of the multiscale renormalization in quantum field theory [PDF]
, 2013 We define in this paper several Hopf algebras describing the combinatorics of the so-called multi-scale renormalization in quantum field theory. After a brief recall of the main mathematical features of multi-scale renormalization, we define assigned ...
Krajewski, Thomas +2 more
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Convex Independence in Permutation Graphs
, 2016 A set C of vertices of a graph is P_3-convex if every vertex outside C has at most one neighbor in C. The convex hull \sigma(A) of a set A is the smallest P_3-convex set that contains A.
B Courcelle +11 more
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Combinatorial Logarithm and Point-Determining Cographs [PDF]
The Electronic Journal of Combinatorics, 2012 We obtain the reduced form of the “combinatorial logarithm” Ω by looking at bijections related to connected point-determining cographs and connected co-point-determining graphs.
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Acyclic and star colorings of cographs
Discrete Applied Mathematics, 2011 An \emph{acyclic coloring} of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of trees. The more restricted notion of \emph{star coloring} requires that the union of any two color classes induces a disjoint collection of stars.
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Asymptotic enumeration of cographs
Electronic Notes in Discrete Mathematics, 2001 Abstract Abstract We consider here labelled and unlabelled cographs, i.e., graphs without induced P4, whose applications are important in computer science and logic, because of their representation by means of parse trees. After a new (analytical) approach for obtaining generating functions associated to parse trees, we solve the open problem of ...
Vlady Ravelomanana, Loÿs Thimonier
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Infinite cographs and chain complete N-free posets
, 2018 We give a necessary and sufficient condition for a $P_4$-free graph to be a cograph. This allows us to obtain a simple proof of the fact that finite $P_4$-free graphs are finite cographs. We also prove that chain complete posets whose comparability graph
Zaguia, Imed
core
Hierarchical Colorings of Cographs
, 2019 Cographs are exactly hereditarily well-colored graphs, i.e., the graphs for which a greedy coloring of every induced subgraph uses only the minimally necessary number of colors $ (G)$. In recent work on reciprocal best match graphs so-called hierarchically coloring play an important role.
Valdivia, D. I. +4 more
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Vizing's conjecture for cographs
, 2016 We show that if $G$ is a cograph, that is $P_4$-free, then for any graph $H$, $ (G\square H)\geq (G) (H)$. By the characterization of cographs as a finite sequence of unions and joins of $K_1$, this result easily follows from that of Bartsalkin and German. However, the techniques used are new and may be useful to prove other results.
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