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The bandwidth problem is finding a linear layout of vertices in a graph in such a way that minimizes the maximum distance between two vertices joined by an edge. The bandwidth problem is one of the classic -complete problems. Especially, the problem is -complete even for trees. The bandwidth problem can be solved in polynomial time for a few graph classes. Efficient...
A graph is König-Egerváry if the size of a minimum vertex cover equals the size of a maximum matching in the graph. We show that the problem of deleting at most k vertices to make a given graph König-Egerváry is fixed-parameter tractable with respect to k. This is proved using interesting structural theorems on matchings and vertex covers which could be useful in other contexts. We also show...
We present the first polynomial-time algorithm to solve the Maximum Weight Independent Set problem for apple-free graphs, which is a common generalization of several important classes where the problem can be solved efficiently, such as claw-free graphs, chordal graphs and cographs. Our solution is based on a combination of two algorithmic techniques (modular decomposition and decomposition by clique...
A graph is chordal if and only if it has no chordless cycle of length more than three. The set of maximal cliques in a chordal graph admits special tree structures called clique trees. A perfect sequence is a sequence of maximal cliques obtained by using the reverse order of repeatedly removing the leaves of a clique tree. This paper addresses the problem of enumerating all the perfect sequences....
From the theory of graph minors we know that the class of planar graphs is the only critical class with respect to tree-width. In the present paper, we reveal a critical class with respect to clique-width, a notion generalizing tree-width. This class is known in the literature under different names, such as unit interval, proper interval or indifference graphs, and has important applications in various...
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