منابع مشابه
2-Partition-Transitive Tournaments
Given a tournament score sequence s1 s2 } } } sn , we prove that there exists a tournament T on vertex set [1, 2, ..., n] such that the degree of any vertex i is si and the subtournaments of T on both the even and the odd vertices are transitive in the given order. This means that i beats j whenever i< j and i# j (mod 2). For any score sequence, we give an algorithm to construct a tournament of...
متن کاملSubdivisions of Transitive Tournaments
We prove that, for r ≥ 2 and n ≥ n(r), every directed graph with n vertices and more edges than the r-partite Turán graph T (r, n) contains a subdivision of the transitive tournament on r + 1 vertices. Furthermore, the extremal graphs are the orientations of T (r, n) induced by orderings of the vertex classes.
متن کاملPan-partition Transitive Realizations
A tournament is an oriented complete graph. There are many conditions that assure that a non increasing sequence s1 ≥ s2 ≥ ... ≥ sn are the scores (out degrees) of the vertices of a tournament. Furthermore, given a realizable score sequence, there are possibly many tournaments that have that sequence as its score sequence. In this paper we explore the existence of realizations of a sequence hav...
متن کاملDomination in transitive colorings of tournaments
An edge coloring of a tournament T with colors 1, 2, . . . , k is called ktransitive if the digraph T (i) defined by the edges of color i is transitively oriented for each 1 ≤ i ≤ k. We explore a conjecture of the first author: For each positive integer k there exists a (least) p(k) such that every k-transitive tournament has a dominating set of at most p(k) vertices. We show how this conjectur...
متن کاملSimple tournaments and sharply transitive groups
If the relation E is transitive, i.e., if (x, y) E E and (y, z) E E imply that (x, z) E E, we speak of a transitive tournament or a total order. Clearly (Z, <) is a total order. We tend to visualize tournaments by considering every edge (x, y) E E as an arrow leading from x to y. In this sense every tournament can also be considered as a complete graph in which every edge is oriented in some di...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1998
ISSN: 0095-8956
DOI: 10.1006/jctb.1997.1806