Hyperbolic Symmetry Settles Rigidity on Higher-Genus Surfaces
Lifting frameworks to the hyperbolic plane turns surface rigidity into a finite gain-graph condition with a 2|V|-edge tightness rule.
Jul 13, 20264 min2607.05023
Combinatorics
math.CODiscrete mathematics, graph theory, enumeration, and optimization.
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Planar Poset Dimension Gets a Linear Obstruction Bound
A structural proof shows that every poset with a planar diagram has dimension at most 96 se(P) + 672.
Jul 13, 20264 min2607.09294
Hamiltonian Digraphs Meet Two-Block Cycle Coloring Bound
A degeneracy argument for $C(k,\ell)$-free Hamiltonian digraphs proves $\chi(D) \leq k+\ell-1$ for $k+\ell \geq 6$, matching lower-bound examples.
Jul 12, 20264 min2607.08664