... and w with the same color. Now the vertex v between u, w on P
4
is not in
C, but since u, w areatdistanceatleast3onC the path uvw together with one of the
u, w-segments of C yields a shorter non-contractible ... preliminaries
Suppose F is a nonempty family of connected bipartite graphs, each with at least 3
vertices. An r-coloring of a graph G is said to be F-free if G contains no 2-...