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16 papers · 1 filter
Unavoidable Induced Subgraph of Infinite 2-connected Graphs
Sarah Allred, Guoli Ding, Bogdan Oporowski
In 1930, Ramsey proved that every infinite graph contains either an infinite clique or an infinite independent set as an induced subgraph. König proved that every infinite graph co…
Complete Minors in Complements of Non-Separating Planar Graphs
Leonard Fowler, Gregory Li, Andrei Pavelescu
We prove that the complement of any non-separating planar graph of order contains a minor, and argue that the order is lowest possible with this property. To il…
Constructions stemming from non-separating planar graphs and their Colin de Verdière invariant
Andrei Pavelescu, Elena Pavelescu
A planar graph is said to be non-separating if there exists an embedding of in such that for any cycle , all vertices of $G\setminus \m…
Simple Graphs of Order 12 and Minimum Degree 6 Contain K_6 Minors
Ryan Odeneal, Andrei Pavelescu
We prove that every simple graph of order 12 which has minimum degree 6 contains a K_6 minor.
The complement of a nIL graph with thirteen vertices is IL
Andrei Pavelescu, Elena Pavelescu
We show that for any simple non-oriented graph G with at least thirteen vertices either G or its complement is intrinsically linked.
Diagonal asymptotics for symmetric rational functions via ACSV
Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle +1
We consider asymptotics of power series coefficients of rational functions of the form where is a symmetric multilinear polynomial. We review a number of such cases from…