5 citations · 6 across the 6 of their papers we have counts for
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Hamiltonicity of planar graphs with a forbidden minor
M. N. Ellingham, Emily A. Marshall, Kenta Ozeki +1
Tutte showed that -connected planar graphs are Hamiltonian, but it is well known that -connected planar graphs need not be Hamiltonian. We show that -minor-free -…
Excluding a large theta graph
Guoli Ding, Emily Marshall
A theta graph, denoted , is a graph of order consisting of a pair of vertices and three independent paths between them of lengths , , and . We provide…
On almost-planar graphs
Guoli Ding, Joshua Fallon, Emily Marshall
A nonplanar graph G is called almost-planar if for every edge e of G, at least one of G\e and G/e is planar. In 1990, Gubser characterized 3-connected almost-planar graphs in his d…
The Characterization of planar, 4-connected, K_{2,5}-minor-free graphs
Emily Abernethy Marshall, Liana Yepremyan, Zach Gaslowitz
We show that every planar, 4-connected, K2;5-minor- free graph is the square of a cycle of even length at least six.
A characterization of -minor-free graphs
M. N. Ellingham, Emily A. Marshall, Kenta Ozeki +1
We provide a complete structural characterization of -minor-free graphs. The -connected -minor-free graphs consist of nine small graphs on at most eight vertic…
Criticality of counterexamples to toroidal edge-hamiltonicity
M. N. Ellingham, Emily A. Marshall
A well-known conjecture of Grünbaum and Nash-Williams proposes that 4-connected toroidal graphs are hamiltonian. The corresponding results for 4-connected planar and projective-pla…