# Mirko Hornák

• 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)
• 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)
• 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.
• 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)
• 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)
• 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)