M. Ellingham

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20242026

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math.CO2025

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…

math.CO2025

Bipartite holes, degree sums and Hamilton cycles

Mark Ellingham, Yixuan Huang, Bing Wei

The {\em bipartite-hole-number} of a graph $G$ , denoted as $I^\pm (G)$ , is the minimum number $k$ such that there exist integers $a$ and $b$ with $a + b = k + 1$ such that for…