Computation of a (canonical) doubly perfect elimination ordering of a doubly chordal graph

1998 ◽  
Vol 5 (2) ◽  
pp. 287-294
Author(s):  
Mahnhoon Lee ◽  
Changhwa Kim
Keyword(s):  
Chordal Graph ◽  
Doubly Chordal Graph ◽  
Doubly Perfect Elimination Ordering ◽  
Perfect Elimination Ordering

scholarly journals An Edge-Signed Generalization of Chordal Graphs, Free Multiplicities on Braid Arrangements, and Their Characterizations

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Takuro Abe ◽  
Koji Nuida ◽  
Yasuhide Numata
Keyword(s):  
Special Kind ◽  
Chordal Graph ◽  
Hyperplane Arrangements ◽  
Chordal Graphs ◽  
Nous Proposons ◽  
Signed Graphs ◽  
International Audience ◽  
Perfect Elimination Ordering

International audience In this article, we propose a generalization of the notion of chordal graphs to signed graphs, which is based on the existence of a perfect elimination ordering for a chordal graph. We give a special kind of filtrations of the generalized chordal graphs, and show a characterization of those graphs. Moreover, we also describe a relation between signed graphs and a certain class of multiarrangements of hyperplanes, and show a characterization of free multiarrangements in that class in terms of the generalized chordal graphs, which generalizes a well-known result by Stanley on free hyperplane arrangements. Finally, we give a remark on a relation of our results with a recent conjecture by Athanasiadis on freeness characterization for another class of hyperplane arrangements. Dans cet article, nous proposons une généralisation de la notion des graphes triangulés à graphes signés, qui est basée sur l'existence d'un ordre d'élimination simplicial à un graphe triangulé. Nous donnons un genre spécial de filtrations des graphes triangulés généralisés, et montrons une caractérisation de ces graphes. De plus, nous décrivons aussi une relation entre graphes signés et une certaine classe de multicompositions d'hyperplans, et montrons une caractérisation de multicompositions libres dans cette classe en termes des graphes triangulés généralisés, qui généralise un résultat célèbre de Stanley sur compositions libres d'hyperplans. Finalement, nous donnons une remarque sur une relation de nos résultats avec une conjecture récente d'Athanasiadis sur une caractérisation du freeness d'une autre classe de compositions d'hyperplans.

Inverse M-matrices completions of then-chordal graph

2005 ◽  
Vol 82 (3) ◽  
pp. 275-288 ◽  
Author(s):  
Xijuan Guo ◽  
Huiping Yao ◽  
Fang Cheng
Keyword(s):  
Chordal Graph

scholarly journals Matrices attaining the minimum semidefinite rank of a chordal graph

2013 ◽  
Vol 438 (10) ◽  
pp. 3804-3816 ◽  
Author(s):  
Naomi Shaked-Monderer
Keyword(s):  
Chordal Graph

scholarly journals Counting and Sampling Markov Equivalent Directed Acyclic Graphs

2019 ◽  
Vol 33 ◽  
pp. 7984-7991
Author(s):  
Topi Talvitie ◽  
Mikko Koivisto
Keyword(s):  
Equivalence Class ◽  
Computational Cost ◽  
Chordal Graph ◽  
Directed Acyclic Graphs ◽  
Desktop Computer ◽  
Bounded Degree ◽  
Acyclic Orientations ◽  
Uniform Sampling ◽  
Acyclic Graphs ◽  
Graph Size

Exploring directed acyclic graphs (DAGs) in a Markov equivalence class is pivotal to infer causal effects or to discover the causal DAG via appropriate interventional data. We consider counting and uniform sampling of DAGs that are Markov equivalent to a given DAG. These problems efficiently reduce to counting the moral acyclic orientations of a given undirected connected chordal graph on n vertices, for which we give two algorithms. Our first algorithm requires O(2nn4) arithmetic operations, improving a previous superexponential upper bound. The second requires O(k!2kk2n) operations, where k is the size of the largest clique in the graph; for bounded-degree graphs this bound is linear in n. After a single run, both algorithms enable uniform sampling from the equivalence class at a computational cost linear in the graph size. Empirical results indicate that our algorithms are superior to previously presented algorithms over a range of inputs; graphs with hundreds of vertices and thousands of edges are processed in a second on a desktop computer.

scholarly journals Finding a Maximum-Weight Convex Set in a Chordal Graph

2019 ◽  
Vol 23 (2) ◽  
pp. 167-190
Author(s):  
Jean Cardinal ◽  
Jean-Paul Doignon ◽  
Keno Merckx
Keyword(s):  
Convex Set ◽  
Chordal Graph ◽  
Maximum Weight

Powers of the Vertex Cover Ideal of a Chordal Graph

2011 ◽  
Vol 39 (10) ◽  
pp. 3753-3764 ◽  
Author(s):  
Fatemeh Mohammadi
Keyword(s):  
Vertex Cover ◽  
Chordal Graph

Coloring squares of graphs via vertex orderings

2020 ◽  
pp. 2050093
Author(s):  
Mehmet Akif Yetim
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Chordal Graph ◽  
Upper Bounds ◽  
Cocomparability Graph ◽  
Vertex Ordering

We provide upper bounds on the chromatic number of the square of graphs, which have vertex ordering characterizations. We prove that [Formula: see text] is [Formula: see text]-colorable when [Formula: see text] is a cocomparability graph, [Formula: see text]-colorable when [Formula: see text] is a strongly orderable graph and [Formula: see text]-colorable when [Formula: see text] is a dually chordal graph, where [Formula: see text] is the maximum degree and [Formula: see text] = max[Formula: see text] is the multiplicity of the graph [Formula: see text]. This improves the currently known upper bounds on the chromatic number of squares of graphs from these classes.

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