5 papers
Equilibria of Inverse-Square Repulsion on the Line Are Arithmetic Progressions
Alper Ferudun
Benjamini asked whether every configuration of points on the real line that is in equilibrium under the inverse-square repulsive force must be an arithmetic progression. Georgakopo…
Three Graffiti.pc Conjectures on Largest Induced Trees: Proofs of Conjectures 141, 142, and 143
Alper Ferudun
For a finite simple graph , let be the largest order of an induced tree and let be the girth. We prove three consecutive conjectures of DeLaViña's Graffiti.pc prog…
Positivity of stretched Littlewood-Richardson coefficients for partitions of length at most five
Alper Ferudun
For partitions lambda, mu, nu the Littlewood-Richardson coefficient stretches to a function P(t) = c(t*nu; t*lambda, t*mu) which, by a theorem of Derksen and Weyman, is a polynomia…
The Erdos n^2/25 max-cut conjecture for small multiples of five, via a per-root-MaxCut envelope and blow-up integrality
Alper Ferudun
Erdős conjectured that every triangle-free graph on vertices can be made bipartite by deleting at most edges; the bound would be sharp, attained by the balanced blow-u…
Exact 6-cut rigidity and small-order superconnectivity for the 6-regular case of Dirac's k=4 problem
Alper Ferudun
Dirac asked in 1970 whether for every k >= 4 there is a k-vertex-critical graph without critical edges; Jensen settled all k >= 5, and only k=4 remains open. Following Skottova and…