9 papers
Strong majority colorings of graphs
Rafał Kalinowski, Mateusz Kamyczura, Monika Pilśniak +1
Motivated by majority vertex-colorings of graphs and digraphs and majority edge-colorings of graphs, we introduce two concepts of strong majority colorings. A strong majority verte…
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…
On rainbow caterpillars in elementary -groups
Sylwia Cichacz, Barbara Krupińska, Mariusz Woźniak
Given a finite Abelian group , consider a tree with vertices. The labeling of the vertices of some graph induces an edge labelin…
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…
A note on sequences variant of irregularity strength for hypercubes
Anna Flaszczyńska, Aleksandra Gorzkowska, Mariusz Woźniak
Let be an edge coloring of the - dimensional hypercube . By the palette at a vertex we mean the sequence $\left(f(e_1(v)), f(e_1(v)),\do…
A note on uniquely embeddable 2-factors
Igor Grzelec, Monika Pilśniak, Mariusz Woźniak
Let be a 2-factor i.e. a vertex-disjoint union of cycles. In this note we completely characterize those 2-factors that are uniquely em…
On decomposing multigraphs into locally irregular submultigraphs
Igor Grzelec, Mariusz Woźniak
A locally irregular multigraph is a multigraph whose adjacent vertices have distinct degrees. The locally irregular edge coloring is an edge coloring of a multigraph such that…
Majority Edge-Colorings of Graphs
Felix Bock, Rafał Kalinowski, Johannes Pardey +3
We propose the notion of a majority -edge-coloring of a graph , which is an edge-coloring of with colors such that, for every vertex of , at most half the edge…