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07/28/2023
Three remarks on 𝐖_2 graphs
Let k ≥ 1. A graph G is 𝐖_𝐤 if for any k pairwise disjoint independent v...
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12/23/2022
Matching Cuts in Graphs of High Girth and H-Free Graphs
The (Perfect) Matching Cut is to decide if a graph has a (perfect) match...
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11/08/2022
Solution to a problem of Katona on counting cliques of weighted graphs
A subset I of the vertex set V(G) of a graph G is called a k-clique inde...
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04/23/2022
Partitioning into degenerate graphs in linear time
Let G be a connected graph with maximum degree Δ≥ 3 distinct from K_Δ + ...
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04/12/2022
1-Extendability of independent sets
In the 70s, Berge introduced 1-extendable graphs (also called B-graphs),...
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01/19/2022
Strengthening a theorem of Meyniel
For an integer k ≥ 1 and a graph G, let 𝒦_k(G) be the graph that has ver...
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11/23/2021
A note on Matching-Cut in P_t-free Graphs
A matching-cut of a graph is an edge cut that is a matching. The problem...
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08/02/2021
Mixing colourings in 2K_2-free graphs
The reconfiguration graph for the k-colourings of a graph G, denoted R_k...
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12/30/2020
The maximum sum of sizes of cross-intersecting families of subsets of a set
A set of sets is called a family. Two families 𝒜 and ℬ of sets are said ...
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08/01/2019
On Cycle Transversals and Their Connected Variants in the Absence of a Small Linear Forest
A graph is H-free if it contains no induced subgraph isomorphic to H. We...
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04/29/2019
Reconfiguring colourings of graphs with bounded maximum average degree
The reconfiguration graph R_k(G) of the k-colourings of a graph G has as...
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02/21/2019
Reconfiguration Graph for Vertex Colourings of Weakly Chordal Graphs
The reconfiguration graph R_k(G) of the k-colourings of a graph G contai...
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02/06/2019
Reconfiguring 10-colourings of planar graphs
Let k ≥ 1 be an integer. The reconfiguration graph R_k(G) of the k-colou...
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10/01/2018
Towards Cereceda's conjecture for planar graphs
The reconfiguration graph R_k(G) of the k-colourings of a graph G has as...
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03/12/2018
Partitioning a graph into degenerate subgraphs
Let G = (V, E) be a graph with maximum degree k≥ 3 distinct from K_k+1. ...
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03/11/2018
Paths between colourings of sparse graphs
The reconfiguration graph R_k(G) of the k-colourings of a graph G has as...
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01/23/2015