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Chordal bipartite, strongly chordal, and strongly chordal bipartite graphs
2003
Discrete Mathematics
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These results motivate a deÿnition of 'strongly chordal bipartite graphs', forming a class intermediate between bipartite interval graphs and chordal bipartite graphs. ...
Strongly chordal (and chordal bipartite) graphs can be similarly characterized in terms of the distribution of triangles (respectively, quadrilaterals). ...
chordal bipartite graphs, and of course every complete bipartite graph is strongly chordal bipartite. ...
doi:10.1016/s0012-365x(02)00674-x
fatcat:fpmoz3jwzjbhrdyupu4xpokkse
Erratum to "Chordal bipartite, strongly chordal, and strongly chordal bipartite graphs"
2003
Discrete Mathematics
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Theorem 5 was not used elsewhere in the paper, except for being erroneously used to motivate the concept of 'strongly chordal bipartite graph' in Section 3. ...
Theorem 5 of the cited paper asserted that a graph is strongly chordal if and only if every k-cycle C is the sum of k − 2 triangles, each of which contains an edge of C. ...
Theorem 5 was not used elsewhere in the paper, except for being erroneously used to motivate the concept of 'strongly chordal bipartite graph' in Section 3. ...
doi:10.1016/s0012-365x(03)00254-1
fatcat:7cvrbmyzgbdmxo3xobgpr364sq
Strongly chordal and chordal bipartite graphs are sandwich monotone
2010
Journal of combinatorial optimization
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In this paper we show that strongly chordal graphs and chordal bipartite graphs are sandwich monotone, answering an open question by Bakonyi and Bono from 1997. ...
In addition, from our results it follows that all strongly chordal graphs and all chordal bipartite graphs with edge constraints can be listed efficiently. ...
Concluding remarks We have proved that strongly chordal graphs and chordal bipartite graphs are sandwich monotone. ...
doi:10.1007/s10878-010-9322-x
fatcat:jgltweclezhsndxe5t6hh4g5sa
Strongly Chordal and Chordal Bipartite Graphs Are Sandwich Monotone
[chapter]
2009
Lecture Notes in Computer Science
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bipartite graphs;
G and G are both strongly chordal By sandwich monotonicity of strongly chordal ⇒ there is an f ∈ F such that G − f strongly chordal Remove all edges in X ⇒ B − f is chordal bipartite ...
: unknown minimum chordal bipartite completion: unknown • Strongly chordal graphs and chordal bipartite graphs are sandwich monotone. recognition problem ⇒ O(min{m log n, n 2 }) Paige and Tarjan 1987, ...
doi:10.1007/978-3-642-02882-3_40
fatcat:ururdu6ekjg3pgaoguqkvwzqcq
Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs
2005
Discrete Applied Mathematics
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This paper deals with the graph isomorphism (GI) problem for two graph classes: chordal bipartite graphs and strongly chordal graphs. ...
It is known that GI problem is GI complete even for some special graph classes including regular graphs, bipartite graphs, chordal graphs, comparability graphs, split graphs, and k-trees with unbounded ...
Acknowledgements The authors are grateful to Jeremy Spinrad, who informed us that the relative complexity of the GI problem on strongly chordal graphs was still open. ...
doi:10.1016/j.dam.2004.06.008
fatcat:fu7cotwjwzgwfiveuzrs5uvr4a
Strongly orderable graphs A common generalization of strongly chordal and chordal bipartite graphs
2000
Discrete Applied Mathematics
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This class of graphs, called strongly orderable graphs, generalizes the strongly chordal graphs and the chordal bipartite graphs in a quite natural way. ...
We consider two characteristic elimination orderings for strongly orderable graphs, one on the vertex set and the second on the edge set, and prove that these graphs can be recognized in O(|V | + |E|)| ...
Acknowledgements The author is grateful to Andreas Brandst adt and Jeremy Spinrad for many useful discussions. ...
doi:10.1016/s0166-218x(99)00149-3
fatcat:lezdqz4b5ffx5pnivdgeoy7upa
On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs
2007
Theoretical Computer Science
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Algorithms 19 (1995) 449-473] on graph sandwich problems published in 1995, left the status of sandwich problems for strongly chordal graphs and chordal bipartite graphs open. ...
We prove that the sandwich problem for strongly chordal graphs is NP-complete. We also give some comments on the computational complexity of the sandwich problem for chordal bipartite graphs. ...
Acknowledgements We are grateful to the referees for their careful reading and many suggestions, which helped to improve the paper. R. ...
doi:10.1016/j.tcs.2007.04.007
fatcat:ijeou6tr5jbytnaqms7eijz3qu
Hamiltonian circuits in chordal bipartite graphs
1996
Discrete Mathematics
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As a corollary, HAMILTONIAN CIRCUIT is NP-complete for strongly chordal split graphs. ...
The main result of this paper is the NP-completeness of the HAMILTONIAN CIRCUIT problem for chordal bipartite graphs. This is proved by a sophisticated reduction from SATISFIABILITY. ...
In this paper we show the NP-completeness of both problems for chordal bipartite graphs, and as a corollary for strongly chordal split graph. ...
doi:10.1016/0012-365x(95)00057-4
fatcat:362pqrhfifgkxjgn3lsmwxh23a
Chordal bipartite completion of colored graphs
2008
Discrete Mathematics
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Sritharan, On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs, Theoret. Comput. ...
Algorithms 19 (1995) 449-473], in their paper on graph sandwich problems published in 1995, left the status of the sandwich problems for strongly chordal graphs and chordal bipartite graphs open. ...
Acknowledgments I thank Atif Abueida for his time and careful listening, Luerbio Faria for the figures, and the anonymous referees for their comments. ...
doi:10.1016/j.disc.2007.06.004
fatcat:2e5z6ep6jfewplqej4qmbuvcge
Chordal- (k,ℓ)and strongly chordal- (k,ℓ)graph sandwich problems
2014
Journal of the Brazilian Computer Society
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Results: We prove that the STRONGLY CHORDAL-(k, ) GRAPH SANDWICH PROBLEM is NP-complete, for k ≥ 1 and ≥ 1, and that the CHORDAL-(k, ) GRAPH SANDWICH PROBLEM is NP-complete, for positive integers k and ...
Particurlarly, we are interested in fully classifying the complexity of this problem when we look to the following properties : 'G is a chordal-(k, )-graph' and 'G is a strongly chordal-(k, )-graph', for ...
Acknowledgements We thank Sritharan for pointing us the result of Dahlhaus and discussing it on Theorem 2 proof. This study is supported by FAPERJ, CNPq and CAPES.
Author details ...
doi:10.1186/s13173-014-0016-6
fatcat:3vxbp6hlvbbixpa3wgtoo6ut2m
Independence complexes of strongly orderable graphs
2022
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
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In particular, we show that if G is a chordal bipartite graph, then Ind(G) is either contractible or homotopy equivalent to a sphere of dimension at least bp(G) − 1. ...
We prove that for any finite strongly orderable (generalized strongly chordal) graph G, the independence complex Ind(G) is either contractible or homotopy equivalent to a wedge of spheres of dimension ...
The class of strongly orderable graphs is firstly introduced by Dahlhaus [5] under the name "generalized strongly chordal graphs" as it constitutes a generalization of strongly chordal graphs and chordal ...
doi:10.31801/cfsuasmas.874855
fatcat:vijoc3o6i5fzjmca7tdpqnsy7i
Graph Sandwich Problems
1995
Journal of Algorithms
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Strongly chordal, chordal bipartite A graph is strongly chordal if it is chordal and contains no sun. A graph is chordal bipartite if it is bipartite and does not contain C n , n ≥ 6. ...
Recognition problems for strongly chordal and chordal bipartite are polynomially equivalent. ...
Homogeneous set A homogeneous set H for a graph G(V, E) is a subset of V such that 1 < |H| < |V| and for all v ∈ V \ H, either (v, h) ∈ E for all h ∈ H or (v, h) / ∈ E for all h ∈ H. ...
doi:10.1006/jagm.1995.1047
fatcat:tvoyqnusgvcs7hgt43arkkvfuq
The i-chords of cycles and paths
2012
Discussiones Mathematicae Graph Theory
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Results include the following: A graph is strongly chordal if and only if, for i ∈ {4, 6}, every cycle C with |V (C)| ≥ i has an (i/2)-chord. ...
A graph is a threshold graph if and only if, for i ∈ {4, 5}, every path P with |V (P )| ≥ i has an (i − 2)-chord. ...
Every ptolemaic graph is strongly chordal [2] (but the strongly chordal graph in Figure 1 is not ptolemaic). ...
doi:10.7151/dmgt.1629
fatcat:b4pmg7fi3neonc4ni7yquo6h6i
Efficient Domination and Efficient Edge Domination: A Brief Survey
[chapter]
2018
Lecture Notes in Computer Science
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ED is solvable in time O(MM) for P 5 -free graphs. chordal
Complexity of Efficient Domination:
strongly chordal
bipartite
chordal bipartite
convex bip.
claw-fr. ...
EED is polynomial for weakly chordal graphs
as well as for permutation graphs and for
chordal bipartite graphs. ...
Corollary. All edges of any C 4 , and all leaf edges of any paw are excluded. All mid-edges of diamond, and all external edges of butterfly are forced. ...
doi:10.1007/978-3-319-74180-2_1
fatcat:dluwxxtpf5al7jrcyy5smoskky
Treewidth of Chordal Bipartite Graphs
1995
Journal of Algorithms
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Chordal bipartite graph are exactly those bipartite graph in which every cycle of length at least six has a chord. ...
We present a polynomial time algorithm for the exact computation of the treewidth of all chordal bipartite graphs. ...
There is a strong connection between chordal bipartite graphs, strongly chordal graphs and totally balanced matrices. ...
doi:10.1006/jagm.1995.1037
fatcat:zrqzyj42brdenir6atgc5bw7ha
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