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Chordal bipartite, strongly chordal, and strongly chordal bipartite graphs

2003
*
Discrete Mathematics
*

These results motivate a deÿnition of '

doi:10.1016/s0012-365x(02)00674-x
fatcat:fpmoz3jwzjbhrdyupu4xpokkse
*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*. ...##
###
Erratum to "Chordal bipartite, strongly chordal, and strongly chordal bipartite graphs"

2003
*
Discrete Mathematics
*

Theorem 5 was not used elsewhere in the paper, except for being erroneously used to motivate the concept of '

doi:10.1016/s0012-365x(03)00254-1
fatcat:7cvrbmyzgbdmxo3xobgpr364sq
*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. ...##
###
Strongly chordal and chordal bipartite graphs are sandwich monotone

2010
*
Journal of combinatorial optimization
*

In this paper we show that

doi:10.1007/s10878-010-9322-x
fatcat:jgltweclezhsndxe5t6hh4g5sa
*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. ...##
###
Strongly Chordal and Chordal Bipartite Graphs Are Sandwich Monotone
[chapter]

2009
*
Lecture Notes in Computer Science
*

*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, ...

##
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Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs

2005
*
Discrete Applied Mathematics
*

This paper deals with the

doi:10.1016/j.dam.2004.06.008
fatcat:fu7cotwjwzgwfiveuzrs5uvr4a
*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. ...##
###
Strongly orderable graphs A common generalization of strongly chordal and chordal bipartite graphs

2000
*
Discrete Applied Mathematics
*

This class of

doi:10.1016/s0166-218x(99)00149-3
fatcat:lezdqz4b5ffx5pnivdgeoy7upa
*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. ...##
###
On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs

2007
*
Theoretical Computer Science
*

Algorithms 19 (1995) 449-473] on

doi:10.1016/j.tcs.2007.04.007
fatcat:ijeou6tr5jbytnaqms7eijz3qu
*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. ...##
###
Hamiltonian circuits in chordal bipartite graphs

1996
*
Discrete Mathematics
*

As a corollary, HAMILTONIAN CIRCUIT is NP-complete for

doi:10.1016/0012-365x(95)00057-4
fatcat:362pqrhfifgkxjgn3lsmwxh23a
*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*. ...##
###
Chordal bipartite completion of colored graphs

2008
*
Discrete Mathematics
*

Sritharan, On the complexity of the sandwich problems for

doi:10.1016/j.disc.2007.06.004
fatcat:2e5z6ep6jfewplqej4qmbuvcge
*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. ...##
###
Chordal- (k,ℓ)and strongly chordal- (k,ℓ)graph sandwich problems

2014
*
Journal of the Brazilian Computer Society
*

Results: We prove that the

doi:10.1186/s13173-014-0016-6
fatcat:3vxbp6hlvbbixpa3wgtoo6ut2m
*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 ...##
###
Independence complexes of strongly orderable graphs

2022
*
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
*

In particular, we show that if G is a

doi:10.31801/cfsuasmas.874855
fatcat:vijoc3o6i5fzjmca7tdpqnsy7i
*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*...##
###
Graph Sandwich Problems

1995
*
Journal of Algorithms
*

*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. ...

##
###
The i-chords of cycles and paths

2012
*
Discussiones Mathematicae Graph Theory
*

Results include the following: A

doi:10.7151/dmgt.1629
fatcat:b4pmg7fi3neonc4ni7yquo6h6i
*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). ...##
###
Efficient Domination and Efficient Edge Domination: A Brief Survey
[chapter]

2018
*
Lecture Notes in Computer Science
*

ED is solvable in time O(MM) for P 5 -free

doi:10.1007/978-3-319-74180-2_1
fatcat:dluwxxtpf5al7jrcyy5smoskky
*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. ...##
###
Treewidth of Chordal Bipartite Graphs

1995
*
Journal of Algorithms
*

*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. ...

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