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- Mirko Hornák, Mariusz Wozniak
- Discrete Mathematics
- 2008

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertexdisjoint subtrees of T whose orders are given by τ ; from a result by Barth and Fournier it follows that ∆(T ) ≤ 4. A necessary and a sufficient condition for being an arbitrarily vertex decomposable star-like tree… (More)

- Keith Edwards, Mirko Hornák, Mariusz Wozniak
- Graphs and Combinatorics
- 2006

- Erik Bruoth, Mirko Hornák
- Discussiones Mathematicae Graph Theory
- 1999

A k-ranking of a graph G is a colouring φ : V (G) → {1, . . . , k} such that any path in G with endvertices x, y fulfilling φ(x) = φ(y) contains an internal vertex z with φ(z) > φ(x). On-line ranking number χ∗ r (G) of a graph G is a minimum k such that G has a k-ranking constructed step by step if vertices of G are coming and coloured one by one in an… (More)

- Ervin Györi, Mirko Hornák, Cory Palmer, Mariusz Wozniak
- Discrete Mathematics
- 2008

It is proved that edges of a graph G can be coloured using χ(G) + 2 colours so that any two adjacent vertices have distinct sets of colours of their incident edges. In the case of a bipartite graph three colours are sufficient.

- Mirko Hornák, Zsolt Tuza, Mariusz Wozniak
- Discrete Applied Mathematics
- 2007

A tree T is arbitrarily vertex decomposable if for any sequence of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by . An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here. © 2007 Elsevier B.V. All rights reserved.

- Mirko Hornák, Mariusz Wozniak
- Discrete Mathematics & Theoretical Computer…
- 2006

Let G be a finite simple graph, let C be a set of colours (in this paper we shall always suppose C ⊆ N) and let f : E(G) → C be an edge colouring of G. The colour set of a vertex v ∈ V (G) with respect to f is the set Sf (v) of colours of edges incident to v. The colouring f is neighbour-distinguishing if it distinguishes any two adjacent vertices by their… (More)

- Hikoe Enomoto, Mirko Hornák
- Journal of Graph Theory
- 2009

- Mirko Hornák, Stanislav Jendrol, Ingo Schiermeyer, Roman Soták
- Journal of Graph Theory
- 2015

In the article, the existence of rainbow cycles in edge colored plane triangulations is studied. It is shown that the minimum number rb(Tn,C3) of colors that force the existence of a rainbow C3 in any n-vertex plane triangulation is equal to 3n−4 2 . For k ≥ 4 a lower bound and for k ∈ {4,5} an upper bound of the number rb(Tn,Ck ) is determined. C © 2014… (More)

- Mirko Hornák, Stanislav Jendrol
- Discussiones Mathematicae Graph Theory
- 1996

The type of a face f of a planar map is a sequence of degrees of vertices of f as they are encountered when traversing the boundary of f . A set T of face types is found such that in any normal planar map there is a face with type from T . The set T has four infinite series of types as, in a certain sense, the minimum possible number. An analogous result is… (More)

- Mirko Hornák, Roman Soták
- Ars Comb.
- 1995