Filters








148 Hits in 10.2 sec

An Efficient Algorithm for Enumerating Chordal Bipartite Induced Subgraphs in Sparse Graphs [article]

Kazuhiro Kurita and Kunihiro Wasa and Hiroki Arimura and Takeaki Uno
2019 arXiv   pre-print
In this paper, we propose a characterization of chordal bipartite graphs and an efficient enumeration algorithm for chordal bipartite induced subgraphs.  ...  Moreover, we propose an algorithm ECB which enumerates all chordal bipartite induced subgraphs in O(ktΔ^2) time per solution on average, where k is the degeneracy, t is the maximum size of K_t,t as an  ...  We consider the number of edges in B[N 1: , the sum of |N (u i )| is at most O(t∆). We next consider the case for 1 ≤ i ≤ d(v) − t.  ... 
arXiv:1903.02161v1 fatcat:dsgsp66xuneaxfzaotnsp3e44e

Defective Ramsey Numbers and Defective Cocolorings in Some Subclasses of Perfect Graphs [article]

Yunus Emre Demirci and Tınaz Ekim and Mehmet Akif Yıldız
2021 arXiv   pre-print
We combine direct proof techniques with our efficient graph generation algorithm to compute several new defective Ramsey numbers in perfect graphs, bipartite graphs and chordal graphs.  ...  We obtain several values for c^𝒢_k(m) in perfect graphs and cographs.  ...  We run Algorithm 1 with these settings and observe that there is no bipartite graph on 18 vertices that has an induced subgraph from T BIP m (1, 4, 9) for m ≥ 14.  ... 
arXiv:2107.12031v1 fatcat:s4waxe2m7be73cnphhiigliyfy

Recent developments on graphs of bounded clique-width

Marcin Kamiński, Vadim V. Lozin, Martin Milanič
2009 Discrete Applied Mathematics  
Whether the clique-width of graphs in a certain class of graphs is bounded or not, is an important question from an algorithmic point of view, as many problems that are NPhard in general admit polynomial-time  ...  Over the last few years, many classes of graphs have been shown to have bounded clique-width. For many others, this parameter has been proved to be unbounded.  ...  This nice decomposability property has led to efficient solutions for many algorithmic graph problems that are NP-hard in general [13] .  ... 
doi:10.1016/j.dam.2008.08.022 fatcat:h45w5c3pfrazbgyfboniyohhha

Graph classes and forbidden patterns on three vertices [article]

Laurent Feuilloley, Michel Habib
2020 arXiv   pre-print
Unfortunately this strategy usually does not lead to an efficient recognition algorithm.  ...  This paper deals with graph classes characterization and recognition. A popular way to characterize a graph class is to list a minimal set of forbidden induced subgraphs.  ...  The first author is thankful to José Correa, Flavio Guinez and Mauricio Soto, for the very first discussions on this topic back in 2013.  ... 
arXiv:1812.05913v3 fatcat:nmuipxm33fbifkjraluex2i3sm

Page 3893 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews  
The results include efficient parallel algorithms for recognizing chordal graphs, finding a maximum clique and a maximum independent set in a chordal graph, finding a breadth-first search tree and a depth  ...  We also show an upper bound of roughly | + Vk —1 on the average degree of linear-sized induced subgraphs of Ramanujan graphs. This compares positively with the classi- cal bound 2k — 1.  ... 

Large Induced Subgraphs via Triangulations and CMSO

Fedor V. Fomin, Ioan Todinca, Yngve Villanger
2015 SIAM journal on computing (Print)  
For a given graph G = (V, E), the task is to maximize |X| subject to the following: there is a set F ⊆ V such that X ⊆ F , the subgraph G[F ] induced by F is of treewidth at most t, and structure (G[F  ...  We obtain an algorithmic meta-theorem for the following optimization problem. Let ϕ be a Counting Monadic Second Order Logic (CMSO) formula and t ≥ 0 be an integer.  ...  Thilikos for fruitful discussions and useful suggestions on the topic of the paper.  ... 
doi:10.1137/140964801 fatcat:zmhblcqudrb5ffkuwmtybcdfye

Treewidth versus clique number. II. Tree-independence number [article]

Clément Dallard, Martin Milanič, Kenny Štorgel
2022 arXiv   pre-print
algorithmic implications for problems related to independent sets.  ...  We define the independence number of a tree decomposition 𝒯 of a graph as the maximum independence number over all subgraphs of G induced by some bag of 𝒯.  ...  Acknowledgements This work is supported in part by the Slovenian Research Agency (I0-0035, research programs P1-0285 and P1-0383, research projects J1-3001, J1-3002, J1-3003, J1-9110, N1-0102, N1-0160,  ... 
arXiv:2111.04543v4 fatcat:65sqtu64wbaxli3mkoyu4tkcfu

Boundary cliques, clique trees and perfect sequences of maximal cliques of a chordal graph [article]

Hisayuki Hara, Akimichi Takemura
2006 arXiv   pre-print
We characterize clique trees of a chordal graph in their relation to simplicial vertices and perfect sequences of maximal cliques.  ...  We describe the relation as a bipartite graph and prove that the bipartite graph is always connected.  ...  This fact is important in enumerating all clique trees for a given chordal graph.  ... 
arXiv:cs/0607055v1 fatcat:5phyhwym6rbrpez7f35gb74p6u

Large induced subgraphs via triangulations and CMSO [article]

Fedor Fomin, Ioan Todinca, Yngve Villanger
2013 arXiv   pre-print
We give an algorithm solving the optimization problem on an n-vertex graph G in time O(#pmc n^t+4 f(t,ϕ)), where #pmc is the number of all potential maximal cliques in G and f is a function depending of  ...  We obtain an algorithmic meta-theorem for the following optimization problem. Let ϕ be a Counting Monadic Second Order Logic (CMSO) formula and t be an integer.  ...  Thilikos for fruitful discussions and useful suggestions on the topic of the paper.  ... 
arXiv:1309.1559v1 fatcat:f6ljhfu3dbdtdf32yr7ljjf4pe

An efficient parallel algorithm for the minimal elimination ordering (MEO) of an arbitrary graph

Elias Dahlhaus, Marek Karpinski
1994 Theoretical Computer Science  
We design the first efficient parallel algorithm for computing the minimal elimination ordering (MEO) of an arbitrary graph.  ...  Karpinski, An efficient parallel algorithm for the minimal elimination ordering (MEO) of an arbitrary graph, Theoretical Computer Science 134 (1994) 493-528.  ...  Acknowledgements Bob Tarjan has raised to us the question of an efficient parallel algorithm for the ME0 Problem. We are thankful to him, and also to Philip Klein for the stimulating discussions.  ... 
doi:10.1016/0304-3975(94)90250-x fatcat:u5whyapbyvdepc4xzo4iszbdxm

Vertex Deletion Parameterized by Elimination Distance and Even Less [article]

Bart M. P. Jansen, Jari J. H. de Kroon, Michał Włodarczyk
2022 arXiv   pre-print
They are related to graph decompositions in which subgraphs that belong to a target class H (e.g., bipartite or planar) are considered simple.  ...  This is applicable to any graph class H for which the corresponding vertex-deletion problem admits a constant-factor approximation algorithm or an FPT algorithm paramaterized by the solution size.  ...  For H defined by a finite set of forbidden induced subgraphs such that Vertex cover is polynomial-time solvable on graphs from H (for example, claw-free graphs), or H ∈ {chordal, bipartite} (for which  ... 
arXiv:2103.09715v4 fatcat:vv3kluwdtjhqdhaflntr6msvdi

New Applications of Clique Separator Decomposition for the Maximum Weight Stable Set Problem [chapter]

Andreas Brandstädt, Van Bang Le, Suhail Mahfud
2005 Lecture Notes in Computer Science  
Graph decompositions such as decomposition by clique separators and modular decomposition are of crucial importance for designing efficient graph algorithms.  ...  In particular, we describe the atom structure for some new classes of graphs whose atoms are P5-free (the P5 is the induced path with 5 vertices) and obtain new polynomial time results for MWS.  ...  For an induced subgraph H of G, a vertex not in H is a k-vertex of H, if it has exactly k neighbors in H. A graph is chordal if it contains no induced cycle C k , k ≥ 4.  ... 
doi:10.1007/11537311_45 fatcat:r2kj7o5sqzhk7mzhyk3kana2a4

Counting the number of independent sets in chordal graphs

Yoshio Okamoto, Takeaki Uno, Ryuhei Uehara
2008 Journal of Discrete Algorithms  
We first provide the following efficient algorithms for a chordal graph: (1) a linear-time algorithm for counting the number of independent sets; (2) a linear-time algorithm for counting the number of  ...  We study some counting and enumeration problems for chordal graphs, especially concerning independent sets.  ...  Acknowledgement The authors thank Masashi Kiyomi for enlightening discussions and pointing out the work by Chang [7] . The authors are grateful to L. Shankar Ram for pointing out a paper [5] .  ... 
doi:10.1016/j.jda.2006.07.006 fatcat:pt3o77gc5zcrhdirjtbnrx5kwe

Linear-Time Counting Algorithms for Independent Sets in Chordal Graphs [chapter]

Yoshio Okamoto, Takeaki Uno, Ryuhei Uehara
2005 Lecture Notes in Computer Science  
We first provide the following efficient algorithms for a chordal graph: (1) a linear-time algorithm for counting the number of independent sets; (2) a linear-time algorithm for counting the number of  ...  We study some counting and enumeration problems for chordal graphs, especially concerning independent sets.  ...  Shankar Ram for pointing out a paper [5] . References  ... 
doi:10.1007/11604686_38 fatcat:dvnk575gnzgyrdcnzombvtlojm

Hardness Results and an Exact Exponential Algorithm for the Spanning Tree Congestion Problem [chapter]

Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno
2011 Lecture Notes in Computer Science  
Additionally, we provide a constant-factor approximation algorithm for cographs, and a linear-time algorithm for chordal cographs. ⋆  ...  This paper studies the complexity of the problem to determine the spanning tree congestion for non-sparse graph classes, while it was investigated for some sparse graph classes before.  ...  Remarks on cographs We showed NP-completeness of STC for graphs of clique-width at most three.  ... 
doi:10.1007/978-3-642-20877-5_44 fatcat:nim2cohsdjewrmawau43sjoysy
« Previous Showing results 1 — 15 out of 148 results