The number of vertices in a digraph G having a particular outdegree (indegree) is called the frequency of the outdegree (indegree). A set f of distinct positive integers {f,, f2,. . . , f n } is the frequency set of the digraph G if every outdegree and indegree occurs with frequency { E F and for ea
In-Tournament Digraphs
β Scribed by J. Bangjensen; J. Huang; E. Prisner
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 859 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract In this paper we introduce a new class of directed graphs called locally semicomplete digraphs. These are defined to be those digraphs for which the following holds: for every vertex __x__ the vertices dominated by __x__ induce a semicomplete digraph and the vertices that dominate __x__
It is proved that every finite digraph of minimum outdegree 3 contains a subdivision of the transitive tournament on 4 vertices.
A tournament is simple if the corresp(!nding reEationa1 system is simple in the alge brnlc ~nse. it ir sh~un that cony F~~utnmlent T,, with IT nodes can be embedded in in simple tourrramant r \*+ 1 apart from two exceptional types of tournaments which can be embeddecl rn a %impie Fournczmtn t TR+ 1.
This paper studies the probability that a random tournament with specified score sequence contains a specified subgraph. The exact asymptotic value is found in the case that the scores are not too far from regular and the subgraph is not too large. An ndimensional saddle-point method is used. As a s