Mike Krebs

collaborators

5 papers

math.CO2026

Chromatic numbers of circulants with indispensable generators

Ferdous Ahmed, David Asraf, David Bonds +5

The Cayley graph $Cay (G, S)$ is the graph whose vertex set is the group $G$ , where two vertices $x$ and $y$ are adjacent if and only if $x y^{- 1}$ or $y x^{- 1}$ lies in some fi…

math.CO2026

Dimensions of Mycielskians of cycles

Brian Chung, Mike Krebs

The Mycielskian is a standard construction studied in many an introductory graph theory course. It is natural to consider Mycielskians of cycles, some of the simplest of all graphs…

math.CO2026

On Matsushita $I ¨ _{1}^{2}$ discrete fundamental groups

Mike Krebs, Alan Pan, Anand Prakash

The Matsushita fundamental groups of a graph $X$ , denoted $I ¨ _{1}^{r} (X)$ , are certain discrete versions of the fundamental group for topological spaces. For $r = 2$ , these groups have a…

math.CO2025

Four plane unit vectors generate a $3$ -colorable graph

Katherine Eng, Timothy Harris, Mike Krebs +2

We show that given an arbitrary set of four plane unit vectors $v_{1}, v_{2}, v_{3}, v_{4}$ , the Cayley graph generated by ${\pm v_{1}, \pm v_{2}, \pm v_{3}, \pm v_{4}}$ is always $3$ -colorable.…

math.CO2025

Chromatic numbers of rank-two Abelian Cayley graphs

Mike Krebs, Alejandro Leyva

A connected Cayley graph for an Abelian group generated by a finite symmetric subset $S$ can be represented by an integer matrix, its Heuberger matrix. We call the number of column…

Chromatic numbers of circulants with indispensable generators

Dimensions of Mycielskians of cycles

On Matsushita I¨12​ discrete fundamental groups

Four plane unit vectors generate a 3-colorable graph

Chromatic numbers of rank-two Abelian Cayley graphs

On Matsushita $I ¨ _{1}^{2}$ discrete fundamental groups

Four plane unit vectors generate a $3$ -colorable graph