6 papers
On the existence of factors intersecting sets of cycles in regular graphs
Jan Goedgebeur, Davide Mattiolo, Giuseppe Mazzuoccolo +3
A recent result by KardoÅ¡, MáÄajová and Zerafa [J. Comb. Theory, Ser. B. 160 (2023) 1--14] related to the famous Berge-Fulkerson conjecture implies that given an arbitrary set…
Manhattan and Chebyshev flows
Lukáš Gáborik, Sascha Kurz, Giuseppe Mazzuoccolo +2
We investigate multidimensional nowhere-zero flows of bridgeless graphs. By extending the established use of the Euclidean norm, this paper considers the Manhattan and Chebyshev no…
Geometric description of -dimensional flows of a graph
Davide Mattiolo, Giuseppe Mazzuoccolo, Jozef RajnÃk +1
A -dimensional nowhere-zero -flow on a graph , an -NZF from now on, is a flow where the value on each edge is an element of whose (Euclidean) norm li…
Expanding vertices to triangles in cubic graphs
Giuseppe Mazzuoccolo, Vahan Mkrtchyan
Contraction of triangles is a standard operation in the study of cubic graphs, as it reduces the order of the graph while typically preserving many of its properties. In this paper…
The Pairing-Hamiltonian property in graph prisms
Marién Abreu, Giuseppe Mazzuoccolo, Federico Romaniello +1
Let be a graph of even order, and consider as the complete graph on the same vertex set as . A perfect matching of is called a pairing of . If for every pairi…
Cubic graphs with edges in exactly one perfect matching
Jan Goedgebeur, Davide Mattiolo, Giuseppe Mazzuoccolo +2
Petersen's seminal work in 1891 asserts that the edge-set of a cubic graph can be covered by distinct perfect matchings if and only if it is bridgeless. Actually, it is known that…