Full rainbow matchings in graphs and hypergraphs
P Gao, R Ramadurai, IM Wanless… - Combinatorics …, 2021 - cambridge.org
Combinatorics, Probability and Computing, 2021•cambridge.org
Let G be a simple graph that is properly edge-coloured with m colours and let\[\mathcal
{M}=\{{M_1},...,{M_m}\}\] be the set of m matchings induced by the colours in G. Suppose
that\[m\leqslant n-{n^ c}\], where\[c> 9/10\], and every matching in\[\mathcal {M}\] has size n.
Then G contains a full rainbow matching, ie a matching that contains exactly one edge from
Mi for each\[1\leqslant i\leqslant m\]. This answers an open problem of Pokrovskiy and gives
an affirmative answer to a generalization of a special case of a conjecture of Aharoni and …
{M}=\{{M_1},...,{M_m}\}\] be the set of m matchings induced by the colours in G. Suppose
that\[m\leqslant n-{n^ c}\], where\[c> 9/10\], and every matching in\[\mathcal {M}\] has size n.
Then G contains a full rainbow matching, ie a matching that contains exactly one edge from
Mi for each\[1\leqslant i\leqslant m\]. This answers an open problem of Pokrovskiy and gives
an affirmative answer to a generalization of a special case of a conjecture of Aharoni and …
Let G be a simple graph that is properly edge-coloured with m colours and let
be the set of m matchings induced by the colours in G. Suppose that
, where
, and every matching in
has size n. Then G contains a full rainbow matching, i.e. a matching that contains exactly one edge from Mi for each
. This answers an open problem of Pokrovskiy and gives an affirmative answer to a generalization of a special case of a conjecture of Aharoni and Berger. Related results are also found for multigraphs with edges of bounded multiplicity, and for hypergraphs.Finally, we provide counterexamples to several conjectures on full rainbow matchings made by Aharoni and Berger.
Cambridge University PressShowing the best result for this search. See all results