Counting subgraphs: a new approach to the Caccetta-Ha¨ggkvist conjecture

We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is Hamiltonian), by Thomassen (every 4-connected line graph is Hamiltonian) and by Fleischner (every cyclically 4-edge-connected cubic graph has either a 3-edge-...

For positive integers n and r we define the Haggkvist-Hell graph, H"n":"r, to be the graph whose vertices are the ordered pairs (h,T) where T is an r-subset of [n], and h is an element of [n] not in T. Vertices (h"x,T"x) and (h"y,T"y) are adjacent iff h"...

Let H be a set of graphs. A graph is called H-free if it does not contain a copy of a member of H as an induced subgraph. If H is a graph then G is called H-free if it is {H}-free. Plummer, Stiebitz, and Toft proved that, for every K"3@?-free graph H on ...