7 citations · 33 across the 16 of their papers we have counts for
7 papers · 2 filters
On two graph isomorphism problems
John Baptist Gauci, Jean Paul Zerafa
In 2015, Bogdanowicz gave a necessary and sufficient condition for a 4-regular circulant graph to be isomorphic to the Cartesian product of two cycles. Accordion graphs, denoted by…
On the existence of graphs which can colour every regular graph
Giuseppe Mazzuoccolo, Gloria Tabarelli, Jean Paul Zerafa
Let and be graphs. An -colouring of is a proper edge-colouring such that for any vertex there exists a vertex with $…
Betwixt and between 2-factor Hamiltonian and Perfect-Matching-Hamiltonian graphs
Federico Romaniello, Jean Paul Zerafa
A Hamiltonian graph is 2-factor Hamiltonian (2FH) if each of its 2-factors is a Hamiltonian cycle. A similar, but weaker, property is the Perfect-Matching-Hamiltonian property (PMH…
Perfect matchings, Hamiltonian cycles and edge-colourings in a class of cubic graphs
Marién Abreu, John Baptist Gauci, Domenico Labbate +2
A graph has the Perfect-Matching-Hamiltonian property (PMH-property) if for each one of its perfect matchings, there is another perfect matching of such that the union of t…
Saved by the rook: a case of matchings and Hamiltonian cycles
Marién Abreu, John Baptist Gauci, Jean Paul Zerafa
The rook graph is a graph whose edges represent all the possible legal moves of the rook chess piece on a chessboard. The problem we consider is the following. Given any set co…
The Erdős--Faber--Lovász Conjecture revisited
John Baptist Gauci, Jean Paul Zerafa
The Erdős--Faber--Lovász Conjecture, posed in 1972, states that if a graph is the union of cliques of order (referred to as defining -cliques) such that two cliques…
Ban--Linial's Conjecture and treelike snarks
Jean Paul Zerafa
A bridgeless cubic graph is said to have a 2-bisection if there exists a 2-vertex-colouring of (not necessarily proper) such that: (i) the colour classes have the same card…