Abstract
AbstractIn this paper we show how to use simple partitioning lemmas in order to embed spanning graphs in a typical member of . Let the maximum density of a graph H be the maximum average degree of all the subgraphs of H. First, we show that for , a graph w.h.p. contains copies of all spanning graphs H with maximum degree at most Δ and maximum density at most d. For , this improves a result of Dellamonica, Kohayakawa, Rödl and Rucińcki. Next, we show that if we additionally restrict the spanning graphs to have girth at least 7 then the random graph contains w.h.p. all such graphs for . In particular, if , the random graph therefore contains w.h.p. every spanning tree with maximum degree bounded by Δ. This improves a result of Johannsen, Krivelevich and Samotij.Finally, in the same spirit, we show that for any spanning graph H with constant maximum degree, and for suitable p, if we randomly color the edges of a graph with colors, then w.h.p. there exists a rainbow copy of H in G (that is, a copy of H with all edges colored with distinct colors). © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 546–564, 2016
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
