42 citations · 162 across the 15 of their papers we have counts for
15 papers · 1 filter
List strong and list normal edge-coloring of (sub)cubic graphs
Borut Lužar, Edita Máčajová, Roman Soták +1
A strong edge-coloring of a graph is a proper edge-coloring, in which the edges of every path of length 3 receive distinct colors; in other words, every pair of edges at distance a…
Locally irregular edge-coloring of subcubic graphs
Borut Lužar, Mária Maceková, Simona Rindošová +3
A graph is {\em locally irregular} if no two adjacent vertices have the same degree. A {\em locally irregular edge-coloring} of a graph is such an (improper) edge-coloring that…
Revisiting Semistrong Edge-Coloring of Graphs
Borut Lužar, Martina Mockovčiaková, Roman Soták
A matching in a graph is {\em semistrong} if every edge of has an endvertex of degree one in the subgraph induced by the vertices of . A {\em semistrong edge-colorin…
Proper conflict-free and unique-maximum colorings of planar graphs with respect to neighborhoods
Igor Fabrici, Borut Lužar, Simona Rindošová +1
A {\em conflict-free coloring} of a graph {\em with respect to open} (resp., {\em closed}) {\em neighborhood} is a coloring of vertices such that for every vertex there is a color…
On the cyclic coloring conjecture
Stanislav Jendrol, Roman Sotak
A cyclic coloring of a plane graph is a coloring of its vertices such that vertices incident with the same face have distinct colors. The minimum number of colors in a cyclic c…
Star Edge-Coloring of Square Grids
Přemysl Holub, Borut Lužar, Erika Mihaliková +2
A star edge-coloring of a graph is a proper edge-coloring without bichromatic paths or cycles of length four. The smallest integer such that admits a star edge-coloring…
On non-repetitive sequences of arithmetic progressions:the cases
Borut Lužar, Martina Mockovčiaková, Pascal Ochem +2
A -subsequence of a sequence is a subsequence , for any positive integer and any , . A \textit{-Thue seque…
Note on 3-Choosability of Planar Graphs with Maximum Degree 4
François Dross, Borut Lužar, Mária Maceková +1
Deciding whether a planar graph (even of maximum degree ) is -colorable is NP-complete. Determining subclasses of planar graphs being -colorable has a long history, but si…
Note on list star edge-coloring of subcubic graphs
Borut Lužar, Martina Mockovčiaková, Roman Soták
{\emph A star edge-coloring} of a graph is a proper edge-coloring without bichromatic paths and cycles of length four. In this paper, we consider the list version of this coloring…
New bounds for locally irregular chromatic index of bipartite and subcubic graphs
Borut Lužar, Jakub Przybyło, Roman Soták
A graph is \textit{locally irregular} if the neighbors of every vertex have degrees distinct from the degree of . \textit{locally irregular edge-coloring} of a graph is…
On incidence coloring conjecture in Cartesian products of graphs
Petr Gregor, Borut Lužar, Roman Soták
An incidence in a graph is a pair where is a vertex of and is an edge of incident to . Two incidences and are adjacent if at least on…
Star edge coloring of some classes of graphs
Ľudmila Bezegová, Borut Lužar, Martina Mockovčiaková +2
\textit{A star edge coloring} of a graph is a proper edge coloring without bichromatic paths and cycles of length four. In this paper we establish tight upper bounds for trees and…
l-facial edge colorings of graphs
Borut Lužar, Martina Mockovčiaková, Roman Soták +2
An l-facial edge coloring of a plane graph is a coloring of the edges such that any two edges at distance at most l on a boundary walk of some face receive distinct colors. It is c…
Strong edge coloring of planar graphs
Dávid Hudák, Borut Lužar, Roman Soták +1
A strong edge coloring of a graph is a proper edge coloring where the edges at distance at most two receive distinct colors. It is known that every planar graph with maximum degree…
Rainbow numbers for graphs with cyclomatic number at most two
Ingo Schiermeyer, Roman Sotak
For a given graph H and n ? 1; let f(n;H) denote the maximum number m for which it is possible to colour the edges of the complete graph Kn with m colours in such a way that each s…