Compositions of Graphs Revisited
نویسندگان
چکیده
منابع مشابه
Compositions of Graphs Revisited
The idea of graph compositions, which was introduced by A. Knopfmacher and M. E. Mays, generalizes both ordinary compositions of positive integers and partitions of finite sets. In their original paper they developed formulas, generating functions, and recurrence relations for composition counting functions for several families of graphs. Here we show that some of the results involving composit...
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An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years. This paper is an attempt at finding a closed-form formula for the number of S-restricted compositions of n. To do so, we reduce the problem to...
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In this paper we introduce a new graph composition, called 2-amalgam, and we prove that the 2-amalgam of perfect graphs is perfect. This composition generalizes many of the operations known to preserve perfection, such as the clique identification, substitution, join and amalgam operations. We give polynominal-time algorithms to determined whether a general graph is decomposable with respect to...
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The concept of a composition of a graph was introduced by Arnold Knopfmacher and M.E. Mays in [2] and denotes a partition of the vertices such that the induced subgraph on each part is connected. Alternatively, a partition can be viewed as the set of connected components of a subgraph including all the vertices of the graph but only a subset of the edges. Most attention hitherto has been devote...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2007
ISSN: 1077-8926
DOI: 10.37236/1016