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Packing subdivisions into regular graphs

We show that, for any graph $F$ and $η>0$, there exists a $d_0=d_0(F,η)$ such that every $n$-vertex $d$-regular graph with $d \geq d_0$ has a collection of vertex-disjoint $F$-subdivisions covering at least $(1-η)n$ vertices. This verifies a conjecture of Verstraëte from 2002 and improves a recent result of Letzter, Methuku and Sudakov which ...
Montgomery, Richard +3 more
openaire +2 more sources

Subdivisions in a bipartite graph

, 2011
Given a bipartite graph G with m and n vertices, respectively,in its vertices classes, and given two integers s, t such that 2 ≤ s ≤ t, 0 ≤ m−s ≤ n−t, and m+n ≤ 2s+t−1, we prove that if G has at least mn−(2(m−s)+n−t) edges then it contains a subdivision of the complete bipartite $K_(s,t)$ with s vertices in the m-class and t vertices in the n-class ...
Balbuena Martínez, Maria Camino Teófila +3 more
openaire +1 more source

Almost optimal geometrically local quantum LDPC codes in any dimension. [PDF]

Nat Commun
Li X, Lin TC, Wills A, Hsieh MH.
europepmc +1 more source

Arboreal networks and their underlying trees. [PDF]

J Math Biol
Huber KT, Overman D.
europepmc +1 more source

Chemical significance and degeneracy of weighted degree-based topological descriptor second Davan index for octane isomers and computation of certain nanostructures. [PDF]