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- Pawel Pralat
- Australasian J. Combinatorics
- 2010

In this paper, we study the vertex pursuit game of Cops and Robbers where cops try to capture a robber loose on the vertices of a graph. The minimum number of cops required to win on a given graph Gâ€¦ (More)

- Margaret-Ellen Messinger, Richard J. Nowakowski, Pawel Pralat
- Theor. Comput. Sci.
- 2008

Following the decontamination metaphor for searching a graph, we introduce a cleaning process, which is related to both the chip-firing game and edge searching. Brushes (instead of chips) are placedâ€¦ (More)

- Anthony Bonato, Noor Hadi, Paul Horn, Pawel Pralat, Changping Wang
- ArXiv
- 2009

On-line social networks such as Facebook or Myspace are of increasing interest to computer scientists, mathematicians, and social scientists alike. In such real-world networks, nodes represent peopleâ€¦ (More)

- Pawel Pralat, Nicholas C. Wormald
- Random Struct. Algorithms
- 2016

In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. Theâ€¦ (More)

- Athanasios Kehagias, Dieter Mitsche, Pawel Pralat
- Theor. Comput. Sci.
- 2013

We examine a version of the Cops and Robber (CR) game in which the robber is invisible, i.e., the cops do not know his location until they capture him. Apparently this game (CiR) has received littleâ€¦ (More)

- Tomasz Luczak, Pawel Pralat
- Random Struct. Algorithms
- 2010

In this paper, we study the vertex pursuit game of Cops and Robbers where cops try to capture a robber on the vertices of the graph. The minimum number of cops required to win on a given graph G isâ€¦ (More)

- Colin S Cooper, Alan M. Frieze, Pawel Pralat
- Internet Mathematics
- 2014

- Serge Gaspers, Margaret-Ellen Messinger, Richard J. Nowakowski, Pawel Pralat
- Inf. Process. Lett.
- 2009

We prove a relationship between the Cleaning problem and the Balanced Vertexâ€“ Ordering problem, namely that the minimum total imbalance of a graph equals twice the brush number of a graph. Thisâ€¦ (More)

- Pawel Pralat, Jacques VerstraÃ«te, Nicholas C. Wormald
- Combinatorica
- 2011

The k-core of a graph is the largest subgraph of minimum degree at least k. We show that for k sufficiently large, the (k + 2)-core of a random graph G(n, p) asymptotically almost surely has aâ€¦ (More)