In this paper, a theorem is proved that generalizes several existing amalgamation results in various ways. The main aim is to disentangle a given edge-colored amalgamated graph so that the result is a graph in which the edges are shared out among the vertices in ways that are fair with respect to several notions of balance (such as between pairs of vertices, degrees of vertices in the both grap...

Motivated by the Frankl’s results in [11] (“Multiply-intersecting families,” J. Combin. Theory (B) 1991), we consider some problems concerning the maximum size of multiply-intersecting families with additional conditions. Among other results, we show the following version of the Erdős–Ko–Rado theorem: for all r ≥ 8 and 1≤ t ≤ 2r+1−3r−1 there exist positive constants ε and n0 such that if n > n0...

The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes which asymptotically achieve capacity on the binary erasure channel (BEC) with bounded complexity, per information bit, of encoding and decoding. It also introduces symmetry properties which play a central role in the construction of capacity-achieving ensembles for the BEC with bounded complexity. The results here impro...