7 citations · 26 across the 38 of their papers we have counts for
10 papers · 1 filter
Rainbow saturation of graphs
António Girão, David Lewis, Kamil Popielarz
In this paper we study the following problem proposed by Barrus, Ferrara, Vandenbussche, and Wenger. Given a graph and an integer , what is $\operatorname{sat}_{t}\left(n, \…
Long cycles in Hamiltonian graphs
António Girão, Teeradej Kittipassorn, Bhargav Narayanan
We prove that if an -vertex graph with minimum degree at least contains a Hamiltonian cycle, then it contains another cycle of length ; this implies, in particular,…
An improved upper bound on the maximum degree of terminal-pairable complete graphs
António Girão, Gábor Mészáros
A graph is terminal-pairable with respect to a demand multigraph on the same vertex set as , if there exists edge-disjoint paths joining the end vertices of every demand…
Partitioning a graph into monochromatic connected subgraphs
António Girão, Shoham Letzter, Julian Sahasrabudhe
A well-known result by Haxell and Kohayakawa states that the vertices of an -coloured complete graph can be partitioned into monochromatic connected subgraphs of distinct co…
Partite Saturation of Complete Graphs
António Girão, Teeradej Kittipassorn, Kamil Popielarz
We study the problem of determining , the minimum number of edges in a -partite graph with vertices in each part such that is -free but the addition…
On the maximum diameter of path-pairable graphs
Antonio Girao, Gabor Meszaros, Kamil Popielarz +1
A graph is path-pairable if for any pairing of its vertices there exist edge disjoint paths joining the vertices in each pair. We obtain sharp bounds on the maximum possible diamet…
Disjoint pairs in set systems with restricted intersection
António Girão, Richard Snyder
The problem of bounding the size of a set system under various intersection restrictions has a central place in extremal combinatorics. We investigate the maximum number of disjoin…
Large induced subgraphs with vertices of almost maximum degree
António Girão, Kamil Popielarz
In this note we prove that for every integer , there exist constants and such that the following holds. If is a graph on vertices with maximum degr…
On the maximum degree of path-pairable planar graphs
António Girão, Gábor Mészáros, Kamil Popielarz +1
A graph is path-pairable if for any pairing of its vertices there exist edge-disjoint paths joining the vertices in each pair. We investigate the behaviour of the maximum degree in…
Generalised Majority Colourings of Digraphs
António Girão, Teeradej Kittipassorn, Kamil Popielarz
The purpose of this note is to draw attention to problems related to a concept called majority colouring recently studied by Kreutzer, Oum, Seymour, van der Zypen and Wood. They ra…