3 papers
math.LO2026
Projective Chromatic Numbers
Adrian Rettich, Luke Serafin
We extend classical notions of definable colourability of graphs to the general projective setting and investigate whether known results, mainly about the dichotomy and the $…
math.CO2024
Roman Domination on Graphings
Adrian Rettich
We study a variant of domination, called Roman domination, where we must assign to each vertex one of the labels 0, 1, or 2 and require that every vertex with label 0 has a neighbo…
math.CO2024
Courcelle's Theorem: A Self-Contained Proof and a Path-Width Variant
Adrian Rettich
Courcelle's Theorem is an important result in graph theory, proving the existence of linear-time algorithms for many decision problems on graphs whose tree-width is bounded by a co…