Abstract
We consider the problem of recognizing graphs containing an f-factor (for any constant f) over the class of partial k-tree complements. We also consider a variation of this problem that only recognizes graphs containing a connected f-factor: this variation generalizes the Hamiltonian circuit problem. We show that these problems have O(n) algorithms for partial k-tree complements (on n vertices); we assume that the Θ(n 2) edges of such a graph are specified by representing the O(n) edges of its complement. As a preliminary result of independent interest, we demonstrate a logical language in which, if a graph property can be expressed over the class of partial k-tree complements, then those graphs that satisfy the property can be recognized in O(n) time.
Research supported by the Natural Sciences and Engineering Research Council of Canada.
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Kaller, D., Gupta, A., Shermer, T. (1995). Regular-factors in the complements of partial k-trees. In: Akl, S.G., Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1995. Lecture Notes in Computer Science, vol 955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60220-8_80
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DOI: https://doi.org/10.1007/3-540-60220-8_80
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