Results 61 to 70 of about 3,632 (158)
Contracting chordal graphs and bipartite graphs to paths and trees
Discrete Applied Mathematics, 2011 Some of the most well studied problems in algorithmic graph theory deal with modifying a graph into an acyclic graph or into a path, using as few operations as possible. In Feedback Vertex Set and Longest Induced Path, the only allowed operation is vertex deletion, and in Spanning Tree and Longest Path, only edge deletions are permitted.
Heggernes, Pinar +3 more
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Journal of Graph Theory, Volume 106, Issue 4, Page 816-842, August 2024.Abstract A minimal separator of a graph G is a set S ⊆ V ( G ) such that there exist vertices a , b ∈ V ( G ) ⧹ S with the property that S separates a from b in G, but no proper subset of S does. For an integer k ≥ 0, we say that a minimal separator is k‐simplicial if it can be covered by k cliques and denote by G k the class of all graphs in which ...
Martin Milanič +3 more
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Strongly orderable graphs A common generalization of strongly chordal and chordal bipartite graphs
Discrete Applied Mathematics, 2000 For a graph \(G = (V,E)\) a linear ordering \(\sigma\) of the vertices is called a strong ordering of \(G\) if the following property is fulfilled: if \(ab, ac, bd \in E\), \(a
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Tree independence number I. (Even hole, diamond, pyramid)‐free graphs
Journal of Graph Theory, Volume 106, Issue 4, Page 923-943, August 2024.Abstract The tree‐independence number tree‐ α, first defined and studied by Dallard, Milanič, and Štorgel, is a variant of treewidth tailored to solving the maximum independent set problem. Over a series of papers, Abrishami et al. developed the so‐called central bag method to study induced obstructions to bounded treewidth.
Tara Abrishami +5 more
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Representation characterizations of chordal bipartite graphs
Journal of Combinatorial Theory, Series B, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Testing versus estimation of graph properties, revisited
Random Structures &Algorithms, Volume 65, Issue 3, Page 460-487, October 2024.Abstract A graph G$$ G $$ on n$$ n $$ vertices is ε$$ \varepsilon $$‐far from property 𝒫 if one should add/delete at least εn2$$ \varepsilon {n}^2 $$ edges to turn G$$ G $$ into a graph satisfying 𝒫. A distance estimator for 𝒫 is an algorithm that given G$$ G $$ and α,ε>0$$ \alpha, \varepsilon >0 $$ distinguishes between the case that G$$ G $$ is (α−ε)$
Asaf Shapira +2 more
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Chordal bipartite completion of colored graphs
Discrete Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Graphs with at most two moplexes
Journal of Graph Theory, Volume 107, Issue 1, Page 38-69, September 2024.Abstract A moplex is a natural graph structure that arises when lifting Dirac's classical theorem from chordal graphs to general graphs. The notion is known to be closely related to lexicographic searches in graphs as well as to asteroidal triples, and has been applied in several algorithms related to graph classes, such as interval graphs, claw‐free ...
Clément Dallard +4 more
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Random Structures &Algorithms, Volume 65, Issue 1, Page 3-16, August 2024.Abstract How many edges in an n$$ n $$‐vertex graph will force the existence of a cycle with as many chords as it has vertices? Almost 30 years ago, Chen, Erdős and Staton considered this question and showed that any n$$ n $$‐vertex graph with 2n3/2$$ 2{n}^{3/2} $$ edges contains such a cycle.
Nemanja Draganić +3 more
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On $P_5$-free Chordal bipartite graphs
, 2017 Presented in ICMCE ...
Aadhavan, S, Renjith, P, Sadagopan, N
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