Pure equality/rainbow interfaces force an independent five-set
We prove an order-free obstruction for a recurrent three-terminal interface in the Earth–Moon problem. Let three independent roots have degree at most q−1, and
The Earth–Moon problem
Mathematics · Graph theory Epoch AI
Created triads and matching palettes in biplanar antiprismatic thickenings
Different changeable edges in an antiprismatic thickening can create disjoint families of independent triples, so a reduction based on deleting one selected tri
Two-fan hub patches in biplanar graphs: a type lemma, mixed-parity choosability, and what blocks an 11-colouring reduction
Local list-colouring reductions are the natural route below the degeneracy bound $\chi\le12$ for biplanar graphs. Recent work showed that many two-fan patches $
Isolated components of critical-graph edge exchange and sharp two-edge escapes
Criticality-preserving edge walks are a natural discovery tool for sparse chromatic obstructions, but a walk from one seed need not explore the full critical-gr