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- Andrzej Grzesik
- J. Comb. Theory, Ser. B
- 2012

- Roman Glebov, Andrzej Grzesik, Tereza Klimosova, Daniel Král
- J. Comb. Theory, Ser. B
- 2015

Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work of researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and… (More)

- Andrzej Grzesik, Hrant Khachatrian
- Discrete Applied Mathematics
- 2014

An edge-coloring of a graph G with colors 1,. .. , t is an interval t-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. In this note we prove that K 1,m,n is interval colorable if… (More)

- Andrzej Grzesik, Ping Hu, Jan Volec
- ArXiv
- 2016

If a graph G has n ≥ 4k vertices and more than n 2 /4 edges, then it contains a copy of C 2k+1. In 1992, Erd˝ os, Faudree and Rousseau showed even more, that the number of edges that occur in a triangle of such a G is at least 2 n/2 + 1, and this bound is tight. They also showed that the minimum number of edges in G that occur in a copy of C 2k+1 for k ≥ 2… (More)

- Andrzej Grzesik
- Discrete Mathematics
- 2012

- Andrzej Grzesik, Tereza Klimovsov'a, Marcin Pilipczuk, Michal Pilipczuk
- 2017

In the classic Maximum Weight Independent Set problem we are given a graph G with a nonnegative weight function on vertices, and the goal is to find an independent set in G of maximum possible weight. While the problem is NP-hard in general, we give a polynomial-time algorithm working on any P6-free graph, that is, a graph that has no path on 6 vertices as… (More)

- Andrzej Grzesik
- Electr. J. Comb.
- 2017

The Caccetta-Häggkvist Conjecture asserts that every oriented graph on n vertices without directed cycles of length less than or equal to l has minimum outdegree at most (n−1)/l. In this paper we state a conjecture for graphs missing a transitive tournament on 2 + 1 vertices, with a weaker assumption on minimum outdegree. We prove that the… (More)

- Andrzej Grzesik, Mirjana Mikalacki, Zoltán Lóránt Nagy, Alon Naor, Balázs Patkós, Fiona Skerman
- Discrete Mathematics & Theoretical Computer…
- 2015

In this paper, we study (1 : b) Avoider-Enforcer games played on the edge set of the complete graph on n vertices. For every constant k ≥ 3 we analyse the k-star game, where Avoider tries to avoid claiming k edges incident to the same vertex. We analyse both versions of Avoider-Enforcer games – the strict and the monotone – and for each provide explicit… (More)

- Andrzej Grzesik, Michal Morayne, Malgorzata Sulkowska
- SIAM J. Discrete Math.
- 2015

We examine the evolution of the best choice algorithm and the probability of its success from a directed path to the linear order of the same cardinality through kth powers of a directed path, 1 ≤ k < n. The vertices of a kth power of a directed path of a known length n are exposed one by one to a selector in some random order. At any time the selector can… (More)

- Andrzej Grzesik, Hrant Khachatrian
- Ninth International Conference on Computer…
- 2013

An edge-coloring of a graph G with colors 1, ..., t is an interval t-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. In this paper we prove that K<sub>1, m, n</sub> is interval… (More)

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