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Extremal results regarding -minors in graphs of girth at least 5
Elad Aigner-Horev, Roi Krakovski
We prove that every 6-connected graph of girth has a -minor and thus settle the Jorgensen conjecture for graphs of girth . Relaxing the assumption on the gir…
Average Degree in Graph Powers
Matt DeVos, Jessica McDonald, Diego Scheide
The kth power of a simple graph G, denoted G^k, is the graph with vertex set V(G) where two vertices are adjacent if they are within distance k in G. We are interested in finding l…
Local chromatic number of quadrangulations of surfaces
Bojan Mohar, Gábor Simonyi, Gábor Tardos
The local chromatic number of a graph was introduced by Erdős et al. [4]. In [17] a connection to topological properties of (a box complex of) the graph was established and in [18]…
A strengthening and a multipartite generalization of the Alon-Boppana-Serre Theorem
Bojan Mohar
The Alon-Boppana theorem confirms that for every and every integer , there are only finitely many -regular graphs whose second largest eigenvalue is at most $2\sqrt…