4 research outputs found
Subsets of vertices of the same size and the same maximum distance
For a simple connected graph and a subset of its vertices, let and let
be the largest such that there are disjoint vertex subsets and of , each of size such that
Let . We prove that for This solves the homometric set problem restricted to the largest distance exactly. In addition we compare with a respective function , where is replaced with
Disjoint induced subgraphs of the same order and size
For a graph , let be the largest integer for which there exist
two vertex-disjoint induced subgraphs of each on vertices, both
inducing the same number of edges. We prove that for
every graph on vertices. This answers a question of Caro and Yuster.Comment: 25 pages, improved presentation, fixed misprints, European Journal of
Combinatoric