21 citations · 92 across the 33 of their papers we have counts for
35 papers
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 Rajník +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…
On the existence of factors intersecting sets of cycles in regular graphs
Jan Goedgebeur, Davide Mattiolo, Giuseppe Mazzuoccolo +3
A recent result by Kardoš, Máčajová and Zerafa [J. Comb. Theory, Ser. B. 160 (2023) 1--14] related to the famous Berge-Fulkerson conjecture implies that given an arbitrary set of o…
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…
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…
On -dimensional nowhere-zero -flows on a graph
Davide Mattiolo, Giuseppe Mazzuoccolo, Jozef Rajník +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…
A lower bound for the complex flow number of a graph: a geometric approach
Davide Mattiolo, Giuseppe Mazzuoccolo, Jozef Rajník +1
Let be a real number. A complex nowhere-zero -flow on a graph is an orientation of together with an assignment such that, for all…
A characterization of graphs with small palette index
Domenico Labbate, Davide Mattiolo, Giuseppe Mazzuoccolo +2
Given an edge-coloring of a graph , we associate to every vertex of the set of colors appearing on the edges incident with . The palette index of is defined as th…
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 $…
Graphs with large palette index
Davide Mattiolo, Giuseppe Mazzuoccolo, Gloria Tabarelli
Given an edge-coloring of a graph, the palette of a vertex is defined as the set of colors of the edges which are incident with it. We define the palette index of a graph as the mi…
On sublinear approximations for the Petersen coloring conjecture
Davide Mattiolo, Giuseppe Mazzuoccolo, Vahan Mkrtchyan
If is a function, then let us say that is sublinear if \[\lim_{n\rightarrow +\infty}\frac{f(n)}{n}=0.\] If is a cubic graph and $…
Some snarks are worse than others
Edita Máčajová, Giuseppe Mazzuoccolo, Vahan Mkrtchyan +1
Many conjectures and open problems in graph theory can either be reduced to cubic graphs or are directly stated for cubic graphs. Furthermore, it is known that for a lot of problem…
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…
An algorithm and new bounds for the circular flow number of snarks
Jan Goedgebeur, Davide Mattiolo, Giuseppe Mazzuoccolo
It is well-known that the circular flow number of a bridgeless cubic graph can be computed in terms of certain partitions of its vertex-set with prescribed properties. In the prese…
Normal -edge-colorings of a family of Loupekhine snarks
Luca Ferrarini, Giuseppe Mazzuoccolo, Vahan Mkrtchyan
In a proper edge-coloring of a cubic graph an edge is called poor or rich, if the set of colors of the edges incident to and contains exactly three or five colors, res…
Normal 6-edge-colorings of some bridgeless cubic graphs
Giuseppe Mazzuoccolo, Vahan Mkrtchyan
In an edge-coloring of a cubic graph, an edge is poor or rich, if the set of colors assigned to the edge and the four edges adjacent it, has exactly five or exactly three distinct…
An equivalent formulation of the Fan-Raspaud Conjecture and related problems
Giuseppe Mazzuoccolo, Jean Paul Zerafa
In 1994, it was conjectured by Fan and Raspaud that every simple bridgeless cubic graph has three perfect matchings whose intersection is empty. In this paper we answer a question…
A unified approach to construct snarks with circular flow number 5
Jan Goedgebeur, Davide Mattiolo, Giuseppe Mazzuoccolo
The well-known 5-flow Conjecture of Tutte, stated originally for integer flows, claims that every bridgeless graph has circular flow number at most 5. It is a classical result that…
Normal edge-colorings of cubic graphs
Giuseppe Mazzuoccolo, Vahan Mkrtchyan
A normal -edge-coloring of a cubic graph is an edge-coloring with colors having the additional property that when looking at the set of colors assigned to any edge and t…
A family of multigraphs with large palette index
Maddalena Avesani, Arrigo Bonisoli, Giuseppe Mazzuoccolo
Given a proper edge-coloring of a loopless multigraph, the palette of a vertex is defined as the set of colors of the edges which are incident with it. The palette index of a multi…
A note on 2--bisections of claw--free cubic graphs
M. Abreu, J. Goedgebeur, D. Labbate +1
A \emph{--bisection} of a bridgeless cubic graph is a --colouring of its vertex set such that the colour classes have the same cardinality and all connected components in…
Colourings of cubic graphs inducing isomorphic monochromatic subgraphs
Marien Abreu, Jan Goedgebeur, Domenico Labbate +1
A -bisection of a bridgeless cubic graph is a -colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two…
Cores, joins and the Fano-flow conjectures
Ligang Jin, Giuseppe Mazzuoccolo, Eckhard Steffen
The Fan-Raspaud Conjecture states that every bridgeless cubic graph has three 1-factors with empty intersection. A weaker one than this conjecture is that every bridgeless cubic gr…