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- Roman Soukal, Premysl Holub
- Electr. J. Comb.
- 2010

The concept of a packing colouring is related to a frequency assignment problem. The packing chromatic number χp(G) of a graph G is the smallest integer k such that the vertex set V (G) can be… (More)

- Jan Ekstein, Jirí Fiala, Premysl Holub, Bernard Lidický
- ArXiv
- 2010

The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set V (G) can be partitioned into disjoint classes X1, . . . , Xk, where vertices in Xi have pairwise… (More)

- Jan Ekstein, Premysl Holub, Olivier Togni
- Discrete Applied Mathematics
- 2014

The packing chromatic number χρ(G) of a graph G is the smallest integer p such that vertices of G can be partitioned into disjoint classes X1, . . . , Xp where vertices in Xi have pairwise distance… (More)

- Premysl Holub, Zdenek Ryjácek, Ingo Schiermeyer, Petr Vrána
- Discrete Mathematics
- 2015

A connected edge-colored graph G is rainbow-connected if any two distinct vertices of G are connected by a path whose edges have pairwise distinct colors; the rainbow connection number rc(G) of G is… (More)

- Premysl Holub, Zdenek Ryjácek, Ingo Schiermeyer
- Discrete Mathematics
- 2015

A connected edge-colored graphG is said to be rainbow-connected if any two distinct vertices of G are connected by a path whose edges have pairwise distinct colors, and the rainbow connection number… (More)

- Jan Ekstein, Premysl Holub, Bernard Lidický
- Discrete Applied Mathematics
- 2012

The packing chromatic number χρ(G) of a graph G is the smallest integer k such that vertices of G can be partitioned into disjoint classes X1, ..., Xk where vertices in Xi have pairwise distance… (More)

- Premysl Holub, Mirka Miller, Hebert Pérez-Rosés, Joseph F. Ryan
- Discrete Applied Mathematics
- 2014

The degree diameter problem involves finding the largest graph (in terms of the number of vertices) subject to constraints on the degree and the diameter of the graph. Beyond the degree constraint… (More)

- Jan Ekstein, Premysl Holub, Tomás Kaiser, Liming Xiong, Shenggui Zhang
- Discrete Mathematics
- 2012

For any positive integer s, a [2, 2s]-factor in a graph G is a connected even factor with maximum degree at most 2s. We prove that if every induced S(K1,2s+1) in a graph G has at least 3 edges in a… (More)

- Nicolas Gastineau, Premysl Holub, Olivier Togni
- ArXiv
- 2017

Although it has recently been proved that the packing chromatic number is unbounded on the class of subcubic graphs, there exists subclasses in which the packing chromatic number is finite (and… (More)

- Premysl Holub, Joseph F. Ryan
- Australasian J. Combinatorics
- 2015

The degree diameter problem involves finding the largest graph (in terms of number of vertices) subject to constraints on the degree and the diameter of the graph. Beyond the degree constraint there… (More)