4 citations · 12 across the 10 of their papers we have counts for
12 papers
The minimum orientable genus of the repeated Cartesian product of graphs
Marietta Galea, John Baptist Gauci
Determining the minimum genus of a graph is a fundamental optimisation problem in the study of network design and implementation as it gives a measure of non-planarity of graphs. I…
A sharp upper bound for the harmonious total chromatic number of graphs and multigraphs
M. Abreu, J. B. Gauci, D. Mattiolo +4
A proper total colouring of a graph is called harmonious if it has the further property that when replacing each unordered pair of incident vertices and edges with their colour…
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…
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…
A note on fractional covers of a graph
John Baptist Gauci, Jean Paul Zerafa
A fractional colouring of a graph is a function that assigns a non-negative real value to all possible colour-classes of containing any vertex of , such that the sum of…
Accordion graphs: Hamiltonicity, matchings and isomorphism with quartic circulants
John Baptist Gauci, Jean Paul Zerafa
Let be a graph of even order and let be the complete graph on the same vertex set of . A pairing of a graph is a perfect matching of the graph . A graph $…
Perfect matchings and Hamiltonicity in the Cartesian product of cycles
John Baptist Gauci, Jean Paul Zerafa
A pairing of a graph is a perfect matching of the complete graph having the same vertex set as . If every pairing of can be extended to a Hamiltonian cycle of the underl…
Extending perfect matchings to Hamiltonian cycles in line graphs
Marién Abreu, John Baptist Gauci, Domenico Labbate +2
A graph admitting a perfect matching has the Perfect-Matching-Hamiltonian property (for short the PMH-property) if each of its perfect matchings can be extended to a Hamiltonian cy…
Existence of regular nut graphs for degree at most 11
Patrick W. Fowler, John Baptist Gauci, Jan Goedgebeur +2
A nut graph is a singular graph with one-dimensional kernel and corresponding eigenverctor with no zero elements. The problem of determining the orders for which -regular nu…
The super-connectivity of Johnson graphs
Gülnaz Boruzanlı Ekinci, John Baptist Gauci
For positive integers and , the uniform subset graph has all -subsets of as vertices and two -subsets are joined by an edge if they…