# Borut Luzar

• Discrete Mathematics
• 2009
An injective coloring of a graph is a vertex coloring where two vertices have distinct colors if a path of length two exists between them. In this paper some results on injective colorings of planarâ€¦ (More)
• 3
• CIAC
• 2010
The linear arboricity la(G) of a graph G is the minimum number of linear forests (graphs where every connected component is a path) that partition the edges of G. In 1984, Akiyama et al. [1] statedâ€¦ (More)
• 1
• Discrete Mathematics
• 2013
A facial parity edge coloring of a 2-edge connected plane graph is an edge coloring where no two consecutive edges of a facial trail of any face receive the same color. Additionally, for every face fâ€¦ (More)
• 1
• Discrete Applied Mathematics
• 2015
An l-facial edge coloring of a plane graph is a coloring of the edges such that any two edges at distance atmost l on a boundarywalk of any face receive distinct colors. It is conjectured that 3 l +â€¦ (More)
• 1
If G is a simple graph, then con(G), the common neighborhood graph of G, has the same vertex set as G, and two vertices of con(G) are adjacent if they have a common neighbor in G. We show that forâ€¦ (More)
• 24
• SIAM J. Discrete Math.
• 2012
For every d â‰¥ 3 and k âˆˆ {2} âˆª [3,âˆž), we determine the smallest Îµ such that every fractional (k + Îµ)-precoloring of vertices at mutual distance at least d of a graph G with fractional chromatic numberâ€¦ (More)