2 citations · 5 across the 7 of their papers we have counts for
8 papers
Proof of a conjecture on isolation of graphs with a universal vertex
Peter Borg, Alastair Farrugia
A copy of a graph is called an -copy. For any graph , the -isolation number of , denoted by , is the size of a smallest subset of the vertex set of …
Factorisations and characterisations of induced-hereditary and compositive properties
A. Farrugia, R. Bruce Richter, G. Semanisin
A graph property (i.e., a set of graphs) is induced-hereditary or additive if it is closed under taking induced-subgraphs or disjoint unions. If $\cP$ and $\cQ$ are properties, the…
Orientable convexity, geodetic and hull numbers in graphs
Alastair Farrugia
We prove three results conjectured or stated by Chartrand, Fink and Zhang [European J. Combin {\bf 21} (2000) 181--189, Disc. Appl. Math. {\bf 116} (2002) 115--126, and pre-print o…
New results on generalized graph coloring
Vladimir E. Alekseev, Alastair Farrugia, Vadim V. Lozin
For graph classes , Generalized Graph Coloring is the problem of deciding whether the vertex set of a given graph can be partitioned into subsets so…
Additive induced-hereditary properties and unique factorization
Grzegorz Arkit, Alastair Farrugia, Peter Mihók +2
We show that additive induced-hereditary properties of coloured hypergraphs can be uniquely factorised into irreducible factors. Our constructions and proofs are so general that th…
Unique factorisation of additive induced-hereditary properties
Alastair Farrugia, R. Bruce Richter
An additive hereditary graph property is a set of graphs, closed under isomorphism and under taking subgraphs and disjoint unions. Let be additive he…