Author:
Balogh József,Csaba Béla,Pluhár András,Treglown Andrew
Abstract
AbstractA perfect Kr-tiling in a graph G is a collection of vertex-disjoint copies of the clique Kr in G covering every vertex of G. The famous Hajnal–Szemerédi theorem determines the minimum degree threshold for forcing a perfect Kr-tiling in a graph G. The notion of discrepancy appears in many branches of mathematics. In the graph setting, one assigns the edges of a graph G labels from {‒1, 1}, and one seeks substructures F of G that have ‘high’ discrepancy (i.e. the sum of the labels of the edges in F is far from 0). In this paper we determine the minimum degree threshold for a graph to contain a perfect Kr-tiling of high discrepancy.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Reference24 articles.
1. [11] Gishboliner, L. , Krivelevich, M. and Michaeli, P. (2020) Colour-biased Hamilton cycles in random graphs. arXiv:2007.12111
2. Packings of graphs and applications to computational complexity
3. [4] Beck, J. and Chen, W. W. L. (1987) Irregularities of Distribution, Vol. 89 of Cambridge Tracts in Mathematics. Cambridge University Press.
4. On the Discrepancies of Graphs
5. The minimum degree threshold for perfect graph packings
Cited by
9 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献