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- DÃ¡vid HudÃ¡k, Borut Luzar, Roman SotÃ¡k, Riste Skrekovski
- Discrete Mathematics
- 2014

- Borut Luzar, Riste Skrekovski, Martin Tancer
- 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)

Fullerene graphs are 3-connected 3-regular planar graphs with only pentagonal and hexagonal faces. We show that the diameter of a fullerene graph G of order n is at least âˆš 24nâˆ’15âˆ’3 6 and at most n/5â€¦ (More)

- Marek Cygan, Lukasz Kowalik, Borut Luzar
- 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)

- Borut Luzar, Riste Skrekovski
- 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)

- Borut Luzar, Martina MockovciakovÃ¡, Roman SotÃ¡k, Riste Skrekovski, Peter Sugerek
- 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)

- Borut Luzar, Zoran Levnajic, Janez Povh, MatjaÅ¾ Perc
- PloS one
- 2014

Interaction among the scientific disciplines is of vital importance in modern science. Focusing on the case of Slovenia, we study the dynamics of interdisciplinary sciences from 1960 to 2010. Ourâ€¦ (More)

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)

- Lukasz Kowalik, Borut Luzar, Riste Skrekovski
- Discrete Mathematics & Theoretical Computerâ€¦
- 2010

We proved that every planar triangle-free graph with n vertices has a subset of vertices that induces a forest of size at least (71n + 72)/128. This improves the earlier work of Salavatipour [10]. Weâ€¦ (More)

- Daniel KrÃ¡l, Matjaz Krnc, Martin Kupec, Borut Luzar, Jan Volec
- 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)