3 papers
math.CO2022
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 .…
math.GT2022
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…
cs.CC2021
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…