Skip to main content
Article thumbnail
Location of Repository

Embedding graphs with bounded degree in sparse pseudorandom graphs

By Y. Kohayakawa, V. Rödl and P. Sissokho

Abstract

In this paper, we show the equivalence of some quasi-random properties for sparse graphs, that is, graphs G with edge density p = |E(G)| / � � n 2 o(1), where o(1) → 0 as n = |V (G) | → ∞. In particular, we prove the following embedding result. For a graph J, write NJ(x) for the neighborhood of the vertex x in J, and let δ(J) and ∆(J) be the minimum and the maximum degree in J. Let H be a triangle-free graph and set dH = max{δ(J): J ⊂ H}. Moreover, put DH = min{2dH, ∆(H)}. Let C> 1 be a fixed constant and suppose p = p(n) ≫ n −1/DH. We show that if G is such that (i) deg G(x) ≤ Cpn for all x ∈ V (G), (ii) for all 2 ≤ r ≤ DH and for all distinct vertices x1,..., xr ∈ V (G), |NG(x1) ∩ · · · ∩ NG(xr) | ≤ Cnp r, (iii) for all but at most o(n 2) pairs {x1, x2} ⊂ V (G), � |NG(x1) ∩ NG(x2) | − np 2 � � = o(np 2), then G contains H as a subgraph. We discuss a setting under which an arbitrary graph H (not necessarily triangle-free) can be embedded in G. We also present an embedding result for directed graphs

Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.135.6253
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.ime.usp.br/~yoshi/M... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.