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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 small section we show by an easy reduction to this problem: Theorem 1 (Damaschke  HAMILTONian circuits in chordal bipartite graphs A graph is said to be chordal bipartite if each of its ...doi:10.1016/0012-365x(95)00057-4 fatcat:362pqrhfifgkxjgn3lsmwxh23a
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. ...
A 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. ...arXiv:2107.04798v1 fatcat:ctb6exbbufgsddv466ic2vvq4q
A 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. ...arXiv:1711.07736v2 fatcat:mtvgwsidcbeczjuo34ttz7m4bu
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.) ...
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. ...
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. ...
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. ...
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. ...
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. ...
Jimbo, A series of identities for the coefficients of inverse matrices on a Hamming scheme (Note) H., 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. ...doi:10.1016/0012-365x(96)90006-0 fatcat:33jltkh5pbbcha6jvjsffnizqy
We show that every 3-tough split 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  . ...doi:10.1016/0012-365x(95)00190-8 fatcat:3vqxxzp2sfc5tlxhqv6xefmt3m
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. ...
We show that the problems STEINER TREE, DOMINATING SET and CONNECTED DOMINATING SET are NP-complete for 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 ...doi:10.1016/0304-3975(87)90067-3 fatcat:kvammiqw2rf43iapl523s5jasq
Finally, we show that under some specific numbering, the transition 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? ...doi:10.1016/j.dam.2008.10.010 fatcat:b34ed2p67bf5fcjs7f34bloupu
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