5 citations · 8 across the 15 of their papers we have counts for
16 papers
On the -dimensional flow number of the Flower snarks
Davide Mattiolo, Jozef Rajník
Let be a real number, a positive integer. A -dimensional nowhere-zero -flow, or -NZF, on a graph is an orientation of together with a function $f\…
On removable edge subsets in graphs with a nowhere-zero -flow
Davide Mattiolo
A set of a graph is -removable if has a nowhere-zero -flow. We prove that every graph admitting a nowhere-zero -flow has a -removable su…
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…
Open problems of the 32nd Workshop on Cycles and Colourings
János Barát, Stijn Cambie, Geňa Hahn +4
Since its beginnings, every Cycles and Colourings workshop holds one or two open problem sessions; this document contains the problems (together with notes regarding the current st…
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…
Solitude patterns of -graphs via CLM's dependence relation
D. V. V. Narayana, D. Mattiolo, Kalyani Gohokar +1
Recently, Goedgebeur, Mazzuoccolo, Renders, Wolf and the second author [Cubic graphs with edges in exactly one perfect matching, J. Graph Theory 112 (2026), 276-289] proved that ev…
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…
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 -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…
Pairwise disjoint perfect matchings in -edge-connected -regular graphs
Yulai Ma, Davide Mattiolo, Eckhard Steffen +1
Thomassen [Problem 1 in Factorizing regular graphs, J. Combin. Theory Ser. B, 141 (2020), 343-351] asked whether every -edge-connected -regular graph of even order has …
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 $…
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…
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…