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- Riste Skrekovski
- Discrete Mathematics
- 2000

- Martin Juvan, Bojan Mohar, Riste Skrekovski
- Combinatorics, Probability & Computing
- 1998

- Daniel Král, Riste Skrekovski
- SIAM J. Discrete Math.
- 2003

- Dávid Hudák, Borut Luzar, Roman Soták, Riste Skrekovski
- Discrete Mathematics
- 2014

- Bojan Mohar, Riste Skrekovski, Heinz-Jürgen Voss
- Journal of Graph Theory
- 2003

Let G be the class of simple planar graphs of minimum degree ≥ 4 in which no two vertices of degree 4 are adjacent. A graph H is light in G if there is a constant w such that every graph in G which has a subgraph isomorphic to H also has a subgraph isomorphic to H whose sum of degrees in G is ≤ w. Then we also write w(H) ≤ w. It is proved that the cycle Cs… (More)

- Lukasz Kowalik, Jean-Sébastien Sereni, Riste Skrekovski
- SIAM J. Discrete Math.
- 2008

The central problem of the total-colorings is the total-coloring conjecture, which asserts that every graph of maximum degree ∆ admits a (∆+2)-total-coloring. Similar to edge-colorings—with Vizing’s edge-coloring conjecture—this bound can be decreased by 1 for plane graphs of higher maximum degree. More precisely, it is known that if ∆ ≥ 10, then every… (More)

- Zdenek Dvorak, Daniel Král, Pavel Nejedlý, Riste Skrekovski
- Eur. J. Comb.
- 2008

Wang and Lih conjectured that for every g ≥ 5, there exists a number M(g) such that the square of a planar graph G of girth at least g and maximum degree ∆ ≥ M(g) is (∆+1)-colorable. The conjecture is known to be true for g ≥ 7 but false for g ∈ {5, 6}. We show that the conjecture for g = 6 is off by just one, i.e., the square of a planar graph G of girth… (More)

- 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 planar graphs with few colors are presented. We show that all planar graphs of girth ≥19 and maximum degree ∆ are injectively ∆-colorable. We also show that all planar… (More)

- Zdenek Dvorak, Bernard Lidický, Riste Skrekovski
- Eur. J. Comb.
- 2011

The Randić index R(G) of a nontrivial connected graph G is defined as the sum of the weights (d(u)d(v))− 1 2 over all edges e = uv ofG. We prove that R(G) ≥ d(G)/2, where d(G) is the diameter of G. This immediately implies that R(G) ≥ r(G)/2, which is the closest result to the well-known Grafiti conjecture R(G) ≥ r(G) − 1 of Fajtlowicz [4], where r(G) is… (More)

The problem of colouring the square of a graph naturally arises in connection with the distance labelings, which have been studied intensively. We consider this problem for sparse subcubic graphs. We show that the choosability χ (G2) of the square of a subcubic graph G of maximum average degree d is at most four if d < 24/11 and G does not contain a… (More)