For a family \mathcal{F} of graphs, a graph G is called \emph{\mathcal{F}-universal} if G contains every graph in \mathcal{F} as a subgraph. Let \mathcal{F}_n(d) be the family of all graphs on n vertices with maximum degree at most d.
Oct 22, 2013
For a family F F of graphs, a graph 𝐺 G is called F F -universal if 𝐺 G contains every graph in F F as a subgraph. Let F 𝑛 ( 𝑑 ) F n ( d ) be the family ...
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Jul 25, 2017 · Abstract:A graph is said to be \mathcal{H}(n, \Delta)-universal if it contains every graph on n vertices with maximum degree at most \Delta.
We prove that asymptotically (as n → ∞ ) almost all graphs with n vertices and C d n 2 − 1 2 d log 1 d n edges are universal with respect to the family ...
Given graphs G and H, an injective function f : V (H) → V (G) is an embedding of H into G if. 1v,ul ∈ E(H) ⇒ 1f(v),f(u)l ∈ E(G) ...
Duration: 1:08:35
Posted: Oct 29, 2018
Posted: Oct 29, 2018
It is proved that asymptotically almost all graphs with n vertices and 10 d edges are universal with respect to the family of all graph with maximum degree ...
Oct 29, 2018 · We focus on the family H(n,d), consisting of all graphs on n vertices with maximum degree bounded by d. We prove that there exists a constant C ...
N. Alon and M. Capalbo, Sparse universal graphs for bounded-degree graphs, Random Structures Algorithms, to appear, 11pp., published on-line in Wiley ...
This thesis investigates the interplay between two branches of discrete mathematics: Ramsey theory and random graphs. The origins of Ramsey theory can ...