arXiv subjects

Leen Droogendijk

Publications and source records attributed to Leen Droogendijk.

2 recordsLinked to original sources

arXiv2024

Nonexistence of certain edge-girth-regular graphs

Edge-girth-regular graphs (abbreviated as \emph{egr} graphs) are regular graphs in which every edge is contained in the same number of shortest cycles. We prove that there is no $3$-regular \emph{egr} graph with girth $7$ such that every edge is on exactly $6$ shortest cycles, and there is no $3$-regular \emph{egr} graph with girth $8$ such that every edge is on exactly $14$ shortest cycles. This was conjectured by Goedgebeur and Jooken. A few other unresolved cases are settled as well.

math.CO↗

arXiv2021

An improved bound on the chromatic number of the Pancake graphs

In this paper an improved bound on the chromatic number of the Pancake graph $P_n, n\geqslant 2$, is presented. The bound is obtained using a subadditivity property of the chromatic number of the Pancake graph. We also investigate an equitable coloring of $P_n$. An equitable $(n-1)$-coloring based on efficient dominating sets is given and optimal equitable $4$-colorings are considered for small $n$. It is conjectured that the chromatic number of $P_n$ coincides with its equitable chromatic number for any $n\geqslant 2$.

math.CO↗