2010/02/08 by Manuel Bodirsky, Bodirsky, Manuel, Diana Piguet +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Limits and Structures in Graph Theory #math.CO
paper · pdf · doi:10.48550/arxiv.1002.1557
8 pages, 1 figure
arxiv created 2010/02/08 · arxiv updated 2010/05/26
We show that the class of finite rooted binary plane trees is a Ramsey class (with respect to topological embeddings that map leaves to leaves). That is, for all such trees P,H and every natural number k there exists a tree T such that for every k-coloring of the (topological) copies of P in T there exists a (topological) copy H' of H in T such that all copies of P in H' have the same color. When the trees are represented by the so-called rooted triple relation, the result gives rise to a Ramsey class of relational structures with respect to induced substructures.