Algorithms for maximum internal spanning tree problem for some graph classes
TL;DR: In this article , the authors proposed linear-time algorithms to compute a maximum internal spanning tree of cographs, block graphs, cactus graphs, chain graphs and bipartite permutation graphs.
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Abstract: For a given graph G, a maximum internal spanning tree of G is a spanning tree of G with maximum number of internal vertices. The Maximum Internal Spanning Tree (MIST) problem is to find a maximum internal spanning tree of the given graph. The MIST problem is a generalization of the Hamiltonian path problem. Since the Hamiltonian path problem is NP-hard, even for bipartite and chordal graphs, two important subclasses of graphs, the MIST problem also remains NP-hard for these graph classes. In this paper, we propose linear-time algorithms to compute a maximum internal spanning tree of cographs, block graphs, cactus graphs, chain graphs and bipartite permutation graphs. The optimal path cover problem, which asks to find a path cover of the given graph with maximum number of edges, is also a well studied problem. In this paper, we also study the relationship between the number of internal vertices in maximum internal spanning tree and number of edges in optimal path cover for the special graph classes mentioned above.
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References
On a class of posets and the corresponding comparability graphs
TL;DR: The comparability graphs of multitrees are characterized and studied with respect to minimal path coverings to generalized to the notion of a multitree.
247
Hamiltonian circuits in chordal bipartite graphs
TL;DR: The main result is the NP-completeness of the HAMILTONIAN CIRCUIT problem for chordal bipartite graphs, proved by a sophisticated reduction from SATISFIABILITY.
166
Either/Or: Using Vertex Cover Structure in Designing FPT-Algorithms — the Case of k-Internal Spanning Tree
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- 30 Jul 2003
TL;DR: This paper studies the parametric dual of this problem, k-Internal Spanning Tree (Does G have a spanning tree with at least k internal vertices?), and gives an algorithm running in time O.
An optimal path cover algorithm for cographs
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TL;DR: This paper presents an optimal algorithm for determining a minimum path cover for a cograph G, and in case G has a Hamiltonian path (cycle) the authors' algorithm exhibits the path ( cycle) as well.
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A linear vertex kernel for maximum internal spanning tree
TL;DR: In this article, a polynomial-time algorithm was proposed to find a spanning tree with at least k internal vertices for any graph G and integer k>=0.
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