منابع مشابه
Tournament minors
We say a digraph G is a minor of a digraph H if G can be obtained from a subdigraph of H by repeatedly contracting a strongly-connected subdigraph to a vertex. Here, we show the class of all tournaments is a well-quasi-order under minor containment.
متن کاملLogarithmically small minors and topological minors
For every integer t there is a smallest real number c(t) such that any graph with average degree at least c(t) must contain a Kt-minor (proved by Mader). Improving on results of Shapira and Sudakov, we prove the conjecture of Fiorini, Joret, Theis and Wood that any graph with n vertices and average degree at least c(t) + ε must contain a Kt-minor consisting of at most C(ε, t) logn vertices. Mad...
متن کاملGraph Minors
For a given graph G and integers b, f ≥ 0, let S be a subset of vertices of G of size b + 1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every graph on n vertices contains at most n/ b+f b such vertex subsets. This result from extremal combinatorics appears to be very useful in the design of several e...
متن کاملBipartite minors
We introduce a notion of bipartite minors and prove a bipartite analog of Wagner’s theorem: a bipartite graph is planar if and only if it does not contain K3,3 as a bipartite minor. Similarly, we provide a forbidden minor characterization for outerplanar graphs and forests. We then establish a recursive characterization of bipartite (2, 2)-Laman graphs — a certain family of graphs that contains...
متن کاملGeneralized whist tournament designs
In this study a new class of tournament designs is introduced. In particular, each game of the tournament involves several (two or more) teams competing against one another. The tournament is also required to satisfy certain balance conditions that are imposed on each pair of players. These balance conditions are related to both the total number of players on each team and the number of teams i...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2015
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2014.12.005