OAR@UM Collection:https://www.um.edu.mt/library/oar/handle/123456789/4052026-06-29T14:39:52Z2026-06-29T14:39:52ZIsolation of connected graphsBorg, Peterhttps://www.um.edu.mt/library/oar/handle/123456789/1462282026-05-07T12:51:22Z2023-01-01T00:00:00ZTitle: Isolation of connected graphs
Authors: Borg, Peter
Abstract: For a connected n-vertex graph G and a positive integer k, let ιk(G) denote the size of a
smallest set D of vertices of G such that the graph obtained from G by deleting the closed
neighbourhood of D contains no connected graph that has at least k edges. By a result of
Caro and Hansberg, ι1(G) ≤ n/3 if n ̸= 2 and G is not a 5-cycle. Let r be the number of
vertices of G that have only one neighbour. We show that ι2(G) ≤ (4n−r)/14 if G is not
a copy of one of six graphs. We also show that ι3(G) ≤ n/4 if G is neither a triangle nor
a 7-cycle. The bounds are sharp. The two new results imply recent results on isolation
of graphs. The bound on ι3(G) strengthens the author’s solution to a problem of Caro
and Hansberg on isolation of cycles.2023-01-01T00:00:00ZSaved by the rook : a case of matchings and Hamiltonian cyclesAbreu, MariénGauci, John BaptistZerafa, Jean Paulhttps://www.um.edu.mt/library/oar/handle/123456789/1434132026-02-03T14:00:55Z2025-01-01T00:00:00ZTitle: Saved by the rook : a case of matchings and Hamiltonian cycles
Authors: Abreu, Marién; Gauci, John Baptist; Zerafa, Jean Paul
Abstract: 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 M containing pairs of
cells such that each cell of the m1×m2 chessboard is in exactly one pair,
we determine the values of the positive integers m1 and m2 for which
it is possible to construct a closed tour of all the cells of the chessboard
which uses all the pairs of cells in M and some edges of the rook graph.
This is an alternative formulation of a graph-theoretical problem presented
in [1] involving the Cartesian product G of two complete graphs
Km1 and Km2 , which is, in fact, isomorphic to the m1×m2 rook graph.
The problem revolves around determining the values of the parameters
m1 and m2 that would allow any perfect matching of the complete graph
on the same vertex set of G to be extended to a Hamiltonian cycle by
using only edges in G.2025-01-01T00:00:00ZAnalytical solutions to the Laplace equation on a hemispherical domainSebu, CristianaAmaira, AndreiPidcock, Michaelhttps://www.um.edu.mt/library/oar/handle/123456789/1425882026-01-08T11:31:41Z2025-01-01T00:00:00ZTitle: Analytical solutions to the Laplace equation on a hemispherical domain
Authors: Sebu, Cristiana; Amaira, Andrei; Pidcock, Michael
Abstract: In this paper, we derive analytical solutions to the Laplace equation in a
hemispherical domain subject to two different idealized Neumann boundary conditions.
The solutions are given as infinite series, and their convergence is analysed.
The theoretical results have been validated by comparing them with numerical results
obtained using EIDORS.2025-01-01T00:00:00ZResearch biography of Jan Boman : mathematician and explorerHasanov, AlemdarKurasov, PavelNovikov, RomanQuinto, Eric ToddSebu, CristianaÖktem, Ozanhttps://www.um.edu.mt/library/oar/handle/123456789/1425862026-01-08T11:16:56Z2025-01-01T00:00:00ZTitle: Research biography of Jan Boman : mathematician and explorer
Authors: Hasanov, Alemdar; Kurasov, Pavel; Novikov, Roman; Quinto, Eric Todd; Sebu, Cristiana; Öktem, Ozan
Abstract: This article provides an overview of Jan Boman’s illustrious seventy year career as an approximation
theorist, microlocal analyst, and integral geometer. We will include his main mathematical themes and some
personal observations.2025-01-01T00:00:00Z