22 citations · 112 across the 37 of their papers we have counts for
28 papers · 1 filter
A rainbow Dirac theorem for loose Hamilton cycles in hypergraphs
Amarja Kathapurkar, Patrick Morris, Guillem Perarnau
A meta-conjecture of Coulson, Keevash, Perarnau and Yepremyan states that above the extremal threshold for a given spanning structure in a (hyper-)graph, one can find a rainbow ver…
The Lonely Runner Conjecture turns 60
Guillem Perarnau, Oriol Serra
The Lonely Runner Conjecture originated in Diophantine approximation is turning 60. Even if the conjecture is still widely open, the flow of partial results, innovative tools and c…
First Order Logic of Sparse Graphs with Given Degree Sequences
Alberto Larrauri, Guillem Perarnau
We consider limit probabilities of first order properties in random graphs with a given degree sequence. Under mild conditions on the degree sequence, we show that the closure set…
A telescopic proof of Cayley's formula
Guillaume Chapuy, Guillem Perarnau
We give a short proof of the fact that the number of labelled trees on vertices is . Although many short proofs are known, we have not seen this one before.
Two lower bounds for -centered colorings
Loïc Dubois, Gwenaël Joret, Guillem Perarnau +2
Given a graph and an integer , a coloring is \emph{-centered} if for every connected subgraph of , either uses more than colors o…
Frozen -colourings of bounded degree graphs
Marthe Bonamy, Nicolas Bousquet, Guillem Perarnau
Let be a graph of maximum degree and be an integer. The -recolouring graph of is the graph whose vertices are -colourings of and where two -colourings…