4 papers
Hadwiger's Conjecture with Certain Forbidden Induced Subgraphs
Daniel Carter
We prove that -free graphs are not counterexamples to Hadwiger's Conjecture, where is any one of 33 graphs on seven, eight, or nine vertices, or .…
An Elementary Proof of the Signature of Satellite Knots
Daniel Carter
We present a proof of Litherland's formula for the Tristram-Levine signature of a satellite knot in terms of its constituents. Litherland's original proof used more advanced algebr…
An Atomic Viewpoint of the TP Completion Problem
Daniel Carter, Charles Johnson
We present two complementary techniques called catalysis and inhibition which allow one to determine if a given pattern is TP completable or TP non-completable, respectively. Empir…
The Complexity of Checking Partial Total Positivity
Daniel Carter, Charles Johnson
We prove that checking if a partial matrix is partial totally positive is co-NP-complete. This contrasts with checking a conventional matrix for total positivity, for which we prov…