منابع مشابه
Acyclic orientations of graphs
Let G be a finite graph with p vertices and x its chromatic polynomial. A combinatorial interpretation is given to the positive integer (-l)px(-A), where h is a positive integer, in terms of acyclic orientations of G. In particular, (-l)Px(-1) is the number of acyclic orientations of G. An application is given to the enumeration of labeled acyclic digraphs. An algebra of full binomial type, in ...
متن کاملRandom acyclic orientations of graphs
II Preface This is a Master's thesis written at the department of Mathematics at the Royal Institute of Technology (KTH) in Stockholm, supervised by Svante Linusson. It is assumed that the reader has studied mathematics at an undergraduate level, and that he is well acquainted with some basic graph theory concepts such as paths and cycles. III Summary This paper is about acyclic orientations of...
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A. Given an undirected graph G = (V, E), and a designated vertex q ∈ V , the notion of a G-parking function (with respect to q) has recently been developed and studied by various authors. This notion generalizes the classical notion of a parking function associated with the complete graph. In this work, we study properties of certain maximum G-parking functions and relate them, in a bije...
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Greene and Zaslavsky proved that the number of acyclic orientations of a graph G with a unique sink at a given vertex is, up to sign, the linear coefficient of the chromatic polynomial. We give three proofs of this result using pure induction, noncommutative symmetric functions, and an algorithmic bijection. We also prove their result that if e=u0v0 is an edge of G then the number of acyclic or...
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A Golomb ruler is a sequence of distinct integers (the markings of the ruler) whose pairwise differences are distinct. Golomb rulers, also known as Sidon sets and B2 sets, can be traced back to additive number theory in the 1930s and have attracted recent research activities on existence problems, such as the search for optimal Golomb rulers (those of minimal length given a fixed number of mark...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1973
ISSN: 0012-365X
DOI: 10.1016/0012-365x(73)90108-8