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Hamiltonian circuits in chordal bipartite graphs

1996
*
Discrete Mathematics
*

As a corollary,

doi:10.1016/0012-365x(95)00057-4
fatcat:362pqrhfifgkxjgn3lsmwxh23a
*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 small section we show by an easy reduction to this problem: Theorem 1 (Damaschke [7]*HAMILTONian**circuits**in**chordal**bipartite**graphs*A*graph*is said to be*chordal**bipartite*if each of its ...##
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Page 2132 of Mathematical Reviews Vol. , Issue 97D
[page]

1997
*
Mathematical Reviews
*

Korner (A-TGRZ; Graz)
974:05203 05C45
Miiller, Haiko (D-FSUMI; Jena)

*Hamiltonian**circuits**in**chordal**bipartite**graphs*. (English summary) Discrete Math. 156 (1996), no. 1-3, 291-298. ... As a corollary,*Hamiltonian**Circuit*is NP-complete for strongly*chordal*split*graphs*. ...##
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Hamiltonicity: Variants and Generalization in P_5-free Chordal Bipartite graphs
[article]

2021
*
arXiv
*
pre-print

A

arXiv:2107.04798v1
fatcat:ctb6exbbufgsddv466ic2vvq4q
*bipartite**graph*is*chordal**bipartite*if every cycle of length at least six has a chord*in*it. ... We also obtain polynomial-time algorithms for treewidth (pathwidth), and minimum fill-*in**in*P_5-free*chordal**bipartite**graph*. ... Hamiltonicity*in*P 5 -free*Chordal**Bipartite**graphs**In*this section, we shall present polynomial-time algorithms for the*Hamiltonian*cycle (path) problem*in*P 5 -free*chordal**bipartite**graphs*. ...##
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On P_5-free Chordal bipartite graphs
[article]

2017
*
arXiv
*
pre-print

A

arXiv:1711.07736v2
fatcat:mtvgwsidcbeczjuo34ttz7m4bu
*bipartite**graph*is*chordal**bipartite*if every cycle of length at least 6 has a chord*in*it. ...*In*this paper, we investigate the structure of P_5-free*chordal**bipartite**graphs*and show that these*graphs*have a Nested Neighborhood Ordering, a special ordering among its vertices. ... Since P 4 -free*chordal**bipartite**graphs*are complete*bipartite**graphs*, the first non-trivial*graph*class*in*this line of research is P 5 -free*chordal**bipartite**graphs*. ...##
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Page 10 of Mathematical Reviews Vol. , Issue 89H
[page]

1989
*
Mathematical Reviews
*

The author proves that /

*chordal**bipartite**graphs*are characterized by a property analogous to one for*chordal**graphs*: A*bipartite**graph*is /*chordal*if and only if for every*circuit*C of length at least ... (The*bipartite**graph*consisting of a 6-*circuit*with one chord shows that the two concepts are not the same.) ...##
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Page 52 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

Informally, a CSG°

*graph*is a complete*graph*, and for k >0, the class of CSG‘*graphs*is defined inductively*in*such a manner that CSG!*graphs*are*chordal**graphs*. ... Let G be an n-extendable, non-*bipartite**graph*with p vertices. ...##
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Page 1393 of Mathematical Reviews Vol. , Issue 98C
[page]

1998
*
Mathematical Reviews
*

The author considers the efficiency of colouring

*chordal**graphs*by the greedy algorithm applied to the ordering of the vertices given by the*Hamiltonian*cycle. ... He shows that this*graph*is*chordal*, which is to say it has a*Hamiltonian*cycle v),---,vU, and there is some divisor d of n! such that v;v; is an edge if and only if vj,yv;.g is an edge. ...##
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Page 4783 of Mathematical Reviews Vol. , Issue 98H
[page]

1998
*
Mathematical Reviews
*

As an application, using the algorithm given earlier, we obtain all

*Hamiltonian**circuits*of a given directed*graph*. ...*In*the case of*bipartite**graphs*this kind of coloring has a number of applications*in*scheduling theory. ...##
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Page 1793 of Mathematical Reviews Vol. , Issue 92d
[page]

1992
*
Mathematical Reviews
*

This paper extends notions of

*chordality*for*bipartite**graphs*with the definition of semichordality. A*graph*is*chordal*if every*circuit*of length > 4 contains a chord. ... A*graph*is*chordal*if and only if it has a perfect elimination scheme.*In*a*bipartite**graph*G, an edge (u,v) is bisimplicial if the neighbors of u and v induce a complete*bipartite*subgraph. ...##
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Page 1793 of Mathematical Reviews Vol. , Issue 92c
[page]

1992
*
Mathematical Reviews
*

This paper extends notions of

*chordality*for*bipartite**graphs*with the definition of semichordality. A*graph*is*chordal*if every*circuit*of length > 4 contains a chord. ... A*graph*is*chordal*if and only if it has a perfect elimination scheme.*In*a*bipartite**graph*G, an edge (u, v) is bisimplicial if the neighbors of u and v induce a complete*bipartite*subgraph. ...##
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Author index to volume 156 (1996)

1996
*
Discrete Mathematics
*

Jimbo, A series of identities for the coefficients of inverse matrices on a Hamming scheme (Note) H.,

doi:10.1016/0012-365x(96)90006-0
fatcat:33jltkh5pbbcha6jvjsffnizqy
*Hamiltonian**circuits**in**chordal**bipartite**graphs*(Note) E., The structure of imperfect critically strongly-imperfect ... Gallian,*Hamiltonian*cycles and paths*in*Cayley*graphs*and digraphs --A survey (Perspectives) K., On a problem concerning piles of counters (Note) H., Kernels*in**graphs*with a clique-cutset (Note) , S. ...##
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Toughness, hamiltonicity and split graphs

1996
*
Discrete Mathematics
*

We show that every 3-tough split

doi:10.1016/0012-365x(95)00190-8
fatcat:3vqxxzp2sfc5tlxhqv6xefmt3m
*graph*is*hamiltonian*and that there is a sequence of nonhamiltonian split*graphs*with toughness converging to 3. ... Furthermore, we present a polynomial time algorithm deciding whether the toughness of a given split*graph*is less than one and show that deciding whether the toughness of a*bipartite**graph*is exactly one ... Moreover, it remains NP-complete when restricted to proper subclasses, namely*chordal**bipartite**graphs*and strongly*chordal*split*graphs*[26] . ...##
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Page 4659 of Mathematical Reviews Vol. , Issue 2002G
[page]

2002
*
Mathematical Reviews
*

The authors reduced Chvatal’s conjecture to the case of weakly

*chordal**graphs*[Part I,*Graphs*Combin. 13 (1997), no. 1, 31-55; MR 97m:05093}.*In*this paper the authors focus on weakly*chordal**graphs*. ... The present authors prove the same result for*Hamiltonian*groups G, that is, finite nonabelian groups*in*which every subgroup is normal. ...##
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The NP-completeness of steiner tree and dominating set for chordal bipartite graphs

1987
*
Theoretical Computer Science
*

We show that the problems STEINER TREE, DOMINATING SET and CONNECTED DOMINATING SET are NP-complete for

doi:10.1016/0304-3975(87)90067-3
fatcat:kvammiqw2rf43iapl523s5jasq
*chordal**bipartite**graphs*. 0304-3975/87/$3.50 @ 1987, Elsevier Science Publishers B.V. ... Therefore, (G,~)EVC. 0 The first author has recently shown by a reduction from 3s~~ that*HAMILTONIAN**CIRCUIT*and IKDEPENDENTDOMINATINGSET areNP-completeforchordalbipartite*graphs*. ... A sequence (x, , . . . , xk) of pairwise distinct vertices*in*V forms a path*in*G if, for all i=l,..., A*graph*G is a*chordal**bipartite**graph*(cbg) if G is*bipartite*and each cycle of G of length greater ...##
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Enumeration aspects of maximal cliques and bicliques

2009
*
Discrete Applied Mathematics
*

Finally, we show that under some specific numbering, the transition

doi:10.1016/j.dam.2008.10.010
fatcat:b34ed2p67bf5fcjs7f34bloupu
*graph*T (G) has a*hamiltonian*path for*chordal*and comparability*graphs*. ... Raynaud, A fast algorithm for building lattices, Information Processing Letters 71 (1999) 199-204] generate maximal bicliques of a*bipartite**graph**in*O(n 2 ) per maximal biclique, where n is the number ... . , C k is a*hamiltonian**circuit*. We close this paper by asking the following questions: (1) Given a*graph*G. Is there a numbering of vertices of G such that the transition*graph*of G is*hamiltonian*? ...
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