1 research outputs found
Short rainbow cycles in graphs and matroids
Let be a simple -vertex graph and be a colouring of with
colours, where each colour class has size at least . We prove that
contains a rainbow cycle of length at most ,
which is best possible. Our result settles a special case of a strengthening of
the Caccetta-H\"aggkvist conjecture, due to Aharoni. We also show that the
matroid generalization of our main result also holds for cographic matroids,
but fails for binary matroids.Comment: 9 pages, 2 figure