2,657 research outputs found
When do two planted graphs have the same cotransversal matroid?
Cotransversal matroids are a family of matroids that arise from planted
graphs. We prove that two planted graphs give the same cotransversal matroid if
and only if they can be obtained from each other by a series of local moves.Comment: 12 pages, 7 figures; expository change
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
Cubic Time Recognition of Cocircuit Graphs of Uniform Oriented Matroids
We present an algorithm which takes a graph as input and decides in cubic
time if the graph is the cocircuit graph of a uniform oriented matroid. In the
affirmative case the algorithm returns the set of signed cocircuits of the
oriented matroid. This improves an algorithm proposed by Babson, Finschi and
Fukuda.
Moreover we strengthen a result of Montellano-Ballesteros and Strausz about
crabbed connectivity of cocircuit graphs of uniform oriented matroids.Comment: 9 page
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