7 papers · 1 filter
Unavoidable substructures in large and infinite -edge-connected graphs
Sarah Allred, M. N. Ellingham
In 1930, Ramsey proved that every large graph contains either a large clique or a large edgeless graph as an induced subgraph. It is well known that every large connected graph con…
Forbidding the subdivided claw as a subgraph or a minor
Sarah Allred, M. N. Ellingham
Let be the subdivided claw, the -vertex tree obtained from a claw by subdividing each edge exactly once. We characterize the graphs (finite and infinite) that do n…
Polynomial invariants of cyclically ordered graphs
Paul Bratch, M. N. Ellingham, Joanna A. Ellis-Monaghan +2
Cyclically ordered graphs, or cogs, sit between abstract graphs and cellularly embedded graphs. They arise naturally in topological graph theory, knot theory, and mathematical biol…
Bipartite holes, degree sums and Hamilton cycles
Mark Ellingham, Yixuan Huang, Bing Wei
The {\em bipartite-hole-number} of a graph , denoted as , is the minimum number such that there exist integers and with such that for…
A Fano framework for embeddings of graphs in surfaces
Blake Dunshee, M. N. Ellingham
We consider seven fundamental properties of cellular embeddings of graphs in compact surfaces, and show that each property can be associated with a point of the Fano plane , in…
Spanning weakly even trees of graphs
Jiangdong Ai, M. N. Ellingham, Zhipeng Gao +5
Let be a graph (with multiple edges allowed) and let be a tree in . We say that is if every leaf of belongs to the same part of the bipartition o…