Projects per year
Abstract
Given graphs ๐น and ๐บ, a perfect ๐นtiling in ๐บ is a collection of vertexdisjoint copies of ๐น in ๐บ that together cover all the vertices in ๐บ. The study of the minimum degree threshold forcing a perfect ๐นtiling in a graph ๐บ has a long history, culminating in the KรผhnโOsthus theorem [D. Kรผhn and D. Osthus, Combinatorica, 29 (2009), pp. 65โ107] which resolves this problem, up to an additive constant, for all graphs ๐น. In this paper we initiate the study of the analogous question for edgeordered graphs. In particular, we characterize for which edgeordered graphs ๐น this problem is welldefined. We also apply the absorbing method to asymptotically determine the minimum degree threshold for forcing a perfect ๐tiling in an edgeordered graph, where ๐ is any fixed monotone path.
Original language  English 

Pages (fromto)  18081839 
Number of pages  32 
Journal  SIAM Journal on Discrete Mathematics 
Volume  38 
Issue number  2 
DOIs  
Publication status  Published  7 Jun 2024 
Keywords
 edgeordered graph
 tilings
 absorbing method
Fingerprint
Dive into the research topics of 'Tiling edgeordered graphs with monotone paths and other structures'. Together they form a unique fingerprint.Projects
 1 Finished

Matchings and tilings in graphs
Engineering & Physical Science Research Council
1/03/21 โ 29/02/24
Project: Research Councils