R. Škrekovski

Publications251
h-index29
Citations2,915
Highly Influential Citations153
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List Improper Colourings of Planar Graphs
  • R. Škrekovski
  • Mathematics
    Combinatorics, Probability and Computing
  • 1 May 1999
A graph G is m-choosable with impropriety d, or simply (m, d)*-choosable, if for every list assignment L, where [mid ]L(v)[mid ][ges ]m for every v∈V(G), there exists an L-colouring of G such that…
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List improper colorings of planar graphs with prescribed girth
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A Theorem about the Channel Assignment Problem
TLDR
All balanced list channel assignment problems (G,L,w) which admit a proper coloring are characterized, which means that each graph with maximum degree $\Delta\ge 2$ has an L(2,1)-labeling using integers $0,\ldots,\Delta^2+\Delta-1$.
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Star Edge Coloring of Some Classes of Graphs
TLDR
Tight upper bounds for trees and subcubic outerplanar graphs are established and an upper bound for outerplanars graphs is derived.
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The Grötzsch Theorem for the Hypergraph of Maximal Cliques
TLDR
The Grotzsch Theorem is extended to list colorings by proving that the clique hypergraph of every planar graph is 3-colorable and 4-choosability of ${\cal H}(G)$ is established for the class of locally planar graphs on arbitrary surfaces.
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List Total Colourings of Graphs
TLDR
The concept of list total colourings is studied and it is proved that every multigraph of maximum degree 3 is 5-total-choosable and the total choice number of a graph is equal to its total chromatic number.
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Cycles Intersecting Edge-Cuts of Prescribed Sizes
TLDR
The concept of a coverable set of integers is introduced and a number of questions are discussed, some of which are related to classical problems of graph theory such as Tutte's $4$-flow conjecture and the Dominating Cycle Conjecture.
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An improved bound on the largest induced forests for triangle-free planar graphs
TLDR
It is proved that every planar triangle-free graph of order n has a subset of vertices that induces a forest of size at least (71n + 72)/128 and poses some questions regarding planar graphs of higher girth.
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Mostar index
We propose and investigate a new bond-additive structural invariant as a measure of peripherality in graphs. We first determine its extremal values and characterize extremal trees and unicyclic…
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Coloring squares of planar graphs with girth six
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