Uniform coverings of 2-paths by 4-paths

Uniform coverings of 2-paths with 5-paths in K2n

We give a construction of a uniform covering of 2-paths with 5-paths in Kn for all even n ≥ 6, i.e., we construct a set S of 5-paths in Kn having the property that each 2-path in Kn lies in exactly one 5-path in S for all even n ≥ 6.

Uniform coverings of 2-paths with 6-cycles in the complete graph

The Ramsey Number of Loose Paths in 3-Uniform Hypergraphs

Recently, asymptotic values of 2-color Ramsey numbers for loose cycles and also loose paths were determined. Here we determine the 2-color Ramsey number of 3-uniform loose paths when one of the paths is significantly larger than the other: for every n > ⌊ 5m 4 ⌋ , we show that R(P n,P m) = 2n + ⌊m + 1 2 ⌋ .

An Algorithm to Obtain Possibly Critical Paths in Imprecise Project Networks

  We consider criticality in project networks having imprecise activity duration times. It is well known that finding all possibly critical paths of an imprecise project network is an NP-hard problem. Here, based on a method for finding critical paths of crisp networks by using only the forward recursion of critical path method, for the first time an algorithm is proposed which can find all pos...

PATH COVERINGS WITH PRESCRIBED ENDS OF THE n−DIMENSIONAL BINARY HYPERCUBE

Let Qn be the n−dimensional binary hypercube, u1, u2 and u3 be distinct even vertices of Qn and v1, v2 and v3 be distinct odd vertices of Qn. We prove that if n ≥ 4, then there exist three paths in Qn, one joining u1 and v1, one joining u2 and u3 and one joining v2 and v3, such that every vertex ofQn belongs to exactly one of the paths.