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

We investigate when limits of graphs (graphons) and permutations (permutons) are uniquely determined by finitely many densities of their substructures, i.e., when they are finitely forcible. Every permuton can be associated with a graphon through the notion of permutation graphs. We find permutons that are finitely forcible but the associated graphons are… (More)

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

- 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 K1,m,n is interval colorable if… (More)

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, Ping Hu, Jan Volec
- ArXiv
- 2016

If a graph G has n ≥ 4k vertices and more than n/4 edges, then it contains a copy of C2k+1. In 1992, Erdős, Faudree and Rousseau showed even more, that the number of edges that occur in a triangle of such a G is at least 2 bn/2c+ 1, and this bound is tight. They also showed that the minimum number of edges in G that occur in a copy of C2k+1 for k ≥ 2… (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
- 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, 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)

- Andrzej Grzesik, Daniel Král, László Miklós Lovász
- Electronic Notes in Discrete Mathematics
- 2017

- 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)