6 research outputs found
Density of Gallai Multigraphs
Diwan and Mubayi asked how many edges of each color could be included in a 33-edge-colored multigraph containing no rainbow triangle. We answer this question under the modest assumption that the multigraphs in question contain at least one edge between every pair of vertices. We also conjecture that this assumption is, in fact, without loss of generality
On a rainbow version of Dirac's theorem
For a collection of not necessarily distinct
graphs on the same vertex set , a graph with vertices in is a
-transversal if there exists a bijection
such that for all . We prove that for
and for each , there exists a
-transversal that is a Hamilton cycle. This confirms a conjecture
of Aharoni. We also prove an analogous result for perfect matchings
Graphs without a rainbow path of length 3
In 1959 Erd\H{o}s and Gallai proved the asymptotically optimal bound for the
maximum number of edges in graphs not containing a path of a fixed length. Here
we study a rainbow version of their theorem, in which one considers
graphs on a common set of vertices not creating a path having edges from
different graphs and asks for the maximal number of edges in each graph. We
prove the asymptotically optimal bound in the case of a path on three edges and
any
Rainbow Generalizations of Ramsey Theory - A Dynamic Survey
In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs
Rainbow Generalizations of Ramsey Theory - A Dynamic Survey
In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs
Rainbow Generalizations of Ramsey Theory - A Dynamic Survey
In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs