What is the largest number where every graph with average degree at least contains a subdivision of ? Mader asked this question in 1967 and was proved by Bollobás and Thomason and independently by Komlós and Szemerédi. This is best possible by considering a disjoint union of . However, this …
The independent domination number of a graph , denoted , is the minimum size of an independent dominating set of . In this talk, we prove a series of results regarding independent domination of graphs with bounded maximum degree. Let be a graph with maximum degree at most where . We prove that …
We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, and (iii) certain random variable on the boundary of a ball has a small tail. As applications, we show that the volume of intersection of …