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Locally Irregular Total Colorings of Graphs
Anna Flaszczyńska, Aleksandra Gorzkowska, Igor Grzelec +2
A total graph is an ordered triple , where are the sets of empty and full vertices, respectively, , and the set of edges is…
Open problems of the 33rd Workshop on Cycles and Colourings
János Barát, Zdeněk Dvořák, Penny Haxell +6
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…
Weak and strong local irregularity of digraphs
Igor Grzelec, Alfréd Onderko, Mariusz Woźniak
Local Irregularity Conjecture states that every simple connected graph, except special cacti, can be decomposed into at most three locally irregular graphs, i.e., graphs in which a…
On Local Irregularity Conjecture for 2-multigraphs
Igor Grzelec, Alfréd Onderko, Mariusz Woźniak
A multigraph in which adjacent vertices have different degrees is called locally irregular. The locally irregular edge coloring is an edge coloring of a multigraph in which eve…
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 a new problem about the local irregularity of graphs
Igor Grzelec, Tomáš Madaras, Alfréd Onderko +1
A graph/multigraph is locally irregular if endvertices of every its edge possess different degrees. The locally irregular edge coloring of is its edge coloring with the pro…
Brooks-type theorem for -hued coloring of graphs
Stanislav Jendroľ, Alfréd Onderko
An -hued coloring of a simple graph is a proper coloring of its vertices such that every vertex is adjacent to at least differently colored vertices. T…