Browsing Combinatorics and Optimization by Author "Levit, Maxwell"

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Extensions of Galvin's Theorem

Levit, Maxwell (University of Waterloo, 2018-04-30)

We discuss problems in list coloring with an emphasis on techniques that utilize oriented graphs. Our central theme is Galvin's resolution of the Dinitz problem (Galvin. J. Comb. Theory, Ser. B 63(1), 1995, 153--158). We ...
Graph Coverings with Few Eigenvalues or No Short Cycles

Levit, Maxwell (University of Waterloo, 2023-05-18)

This thesis addresses the extent of the covering graph construction. How much must a cover X resemble the graph Y that it covers? How much can X deviate from Y? The main statistics of X and Y which we will measure are their ...
On Eulerian orientations of even-degree hypercubes

Levit, Maxwell; Chandran, L. Sunil; Cheriyan, Joseph (Elsevier, 2018-09-01)

It is well known that every Eulerian orientation of an Eulerian 2k-edge connected (undirected) graph is strongly k-edge connected. A long-standing goal in the area is to obtain analogous results for other types of connectivity, ...