1 research outputs found
Counting K_4-Subdivisions
A fundamental theorem in graph theory states that any 3-connected graph
contains a subdivision of . As a generalization, we ask for the minimum
number of -subdivisions that are contained in every -connected graph on
vertices. We prove that there are such -subdivisions and
show that the order of this bound is tight for infinitely many graphs. We
further investigate a better bound in dependence on and prove that the
computational complexity of the problem of counting the exact number of
-subdivisions is -hard.Comment: 5 figure