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Title:ÌýWhen all holes have the same length

Abstract:Ìý´¡ hole is an induced cycle of length at least 4. For an integer k ≥ 4, we denote by Ck, the class of graphs where every hole has length k. We have defined a new class of graphs named blowup of â„“-templates whose all holes have length 2â„“ + 1. Using earlier results on other related classes of graphs, we did obtain the following structural theorem :

Title:ÌýGenerating k EPR-pairs from an n-party resource state

Abstract:ÌýMotivated by quantum network applications over classical channels, we initiate the study of n-party resource states from which LOCC protocols can create EPR-pairs between any k disjoint pairs of parties.

Title:ÌýProbabilistic root finding in code-based cryptography

Abstract:ÌýFactorization of polynomials over finite fields, and the particularÌýsubproblem of finding roots of polynomials, have many applications in diverse areas such as computer algebra, cryptography and codingÌýtheory, among many others. In practice, fast factorization algorithms are probabilistic.

Title:ÌýSome results on spectralÌýTurán's type problem

Title:ÌýCoinvariants and superspace

Title:ÌýNew Eigenvalue Bound for the Fractional Chromatic Number

Title:ÌýFrom the nabla operator to the super nabla operator

Title:ÌýOn edge-transitive distance-regular antipodal covers of complete graphs

Title: Nash-Williams Orientation Conjecture for Infinite Graphs ÌýÌýÌýÌýÌýÌý

Abstract: In 1960 Nash-Williams proved that every 2k-edge-connected finite graph admits a k-arc-connected orientation. He conjectured that this isÌý also true for infinite graphs. We try to prove the conjecture. Joint work with Bruce Richter.

Title: Extended Formulations