In this paper we study a fundamental open problem in the area of probabilistic checkable proofs: What is the smallest s such that NP naPCP1,s[O(log n), 3]? In the language of har...
We present a verified enumeration of tame graphs as defined in Hales' proof of the Kepler Conjecture and confirm the completeness of Hales' list of all tame graphs while ...
Recently, a mathematical proof is obtained in (Liu, Chiu, Xu, 2004) on the so called one-bit-matching conjecture that all the sources can be separated as long as there is an one-to...
Egecioglu and Remmel [2] gave an interpretation for the entries of the inverse Kostka matrix K-1 in terms of special rim-hook tableaux. They were able to use this interpretation to...
We study here the spectra of random lifts of graphs. Let G be a finite connected graph, and let the infinite tree T be its universal cover space. If λ1 and ρ are the spectral ...