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A rainbow Dirac's theorem
(2020-01-01)
Article
Open AccessA famous theorem of Dirac states that any graph on n vertices with minimum degree at least n/2 has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this result, we show the existence of rainbow Hamilton ... -
Enumeration of labelled 4-regular planar graphs
(2019-08-01)
Article
Open AccessWe present the first combinatorial scheme for counting labelled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4-regular ... -
Further results on random cubic planar graphs
(2020-06)
Article
Restricted access - publisher's policyWe provide precise asymptotic estimates for the number of several classes of labeled cubic planar graphs, and we analyze properties of such random graphs under the uniform distribution. This model was first analyzed by ... -
Maximal independent sets and maximal matchings in series-parallel and related graph classes
(2020-01-10)
Article
Open AccessThe goal of this paper is to obtain quantitative results on the number and on the size of maximal independent sets and maximal matchings in several block-stable graph classes that satisfy a proper sub-criticality condition. ... -
Fixed subgroups and computation of auto-fixed closures in free-abelian times free groups
(2020-04-01)
Article
Open AccessThe classical result by Dyer–Scott about fixed subgroups of finite order automor-phisms of Fnbeing free factors of Fn is no longer true inZm×Fn. Within this more generalcontext, we prove a relaxed version in the spirit of ...
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