Michael Lafferty

most citedA Note on Odd Colorings of 1-Planar Graphs

22 citations · 22 across the 4 of their papers we have counts for

collaborators

4 papers

math.CO2025

Connectivity of contraction-critical graphs

Michael Lafferty, Runrun Liu, Martin Rolek +1

Contraction-critical graphs came from the study of minimal counterexamples to Hadwiger's conjecture. A graph is $k$ -contraction-critical if it is $k$ -chromatic, but any proper mino…

math.CO2022

Every graph with no $K_{9}^{- 6}$ minor is $8$ -colorable

Michael Lafferty, Zi-Xia Song

For positive integers $t$ and $s$ , let $K_{t}^{- s}$ denote the family of graphs obtained from the complete graph $K_{t}$ by removing $s$ edges. A graph $G$ has no $\mathcal{K…

math.CO2022

Every graph with no $K_{8}^{- 4}$ minor is $7$ -colorable

Michael Lafferty, Zi-Xia Song

Hadwiger's Conjecture from 1943 states that every graph with no $K_{t}$ minor is $(t - 1)$ -colorable; it remains wide open for all $t \geq 7$ . For positive integers $t$ and $s$ , let $\…

math.CO2022★ 22 cited

A Note on Odd Colorings of 1-Planar Graphs

Daniel W. Cranston, Michael Lafferty, Zi-Xia Song

A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an odd number of times on its neighborhood. This notion was recently introduced by Petr…

Connectivity of contraction-critical graphs

Every graph with no K9−6​ minor is 8-colorable

Every graph with no K8−4​ minor is 7-colorable

A Note on Odd Colorings of 1-Planar Graphs

Every graph with no $K_{9}^{- 6}$ minor is $8$ -colorable

Every graph with no $K_{8}^{- 4}$ minor is $7$ -colorable