
On P_5free Chordal bipartite graphs
A bipartite graph is chordal bipartite if every cycle of length at least...
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Hamiltonian Path in Split Graphs a Dichotomy
In this paper, we investigate Hamiltonian path problem in the context of...
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Backtracking (the) Algorithms on the Hamiltonian Cycle Problem
Even though the Hamiltonian cycle problem is NPcomplete, many of its pr...
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Hamiltonicity in Convex Bipartite Graphs
For a connected graph, the Hamiltonian cycle (path) is a simple cycle (p...
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Isolation schemes for problems on decomposable graphs
The Isolation Lemma of Mulmuley, Vazirani and Vazirani [Combinatorica'87...
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Propagating Conjunctions of AllDifferent Constraints
We study propagation algorithms for the conjunction of two AllDifferent ...
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Fair packing of independent sets
In this work we add a graph theoretical perspective to a classical probl...
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Hamiltonicity: Variants and Generalization in P_5free Chordal Bipartite graphs
A bipartite graph is chordal bipartite if every cycle of length at least six has a chord in it. Müller <cit.> has shown that the Hamiltonian cycle problem is NPcomplete on chordal bipartite graphs by presenting a polynomialtime reduction from the satisfiability problem. The microscopic view of the reduction instances reveals that the instances are P_9free chordal bipartite graphs, and hence the status of Hamiltonicity in P_8free chordal bipartite graphs is open. In this paper, we identify the first nontrivial subclass of P_8free chordal bipartite graphs which is P_5free chordal bipartite graphs, and present structural and algorithmic results on P_5free chordal bipartite graphs. We investigate the structure of P_5free chordal bipartite graphs and show that these graphs have a Nested Neighborhood Ordering (NNO), a special ordering among its vertices. Further, using this ordering, we present polynomialtime algorithms for classical problems such as the Hamiltonian cycle (path), also the variants and generalizations of the Hamiltonian cycle (path) problem. We also obtain polynomialtime algorithms for treewidth (pathwidth), and minimum fillin in P_5free chordal bipartite graph. We also present some results on complement graphs of P_5free chordal bipartite graphs.
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