Given a graph G, a set of spanning trees of G are completely independent if for any vertices x and y, the paths connecting them on these trees have neither vertex nor edge in common, except x and y. In this paper, we prove that for graphs of order n, with n ≥ 6, if the minimum degree is at least n-2, then there are at least ⌊n/3⌋ completely independent spanning trees.

Packet classification is important in fulfilling the requirements of differentiated services in next generation networks. One of interesting hardware solutions proposed to solve the packet classification problem is bit vector algorithm. Different from other hardware solutions such as ternary CAM, it efficiently utilizes the memories to achieve an excellent performance in medium size policy database; however, it exhibits poor worst-case performance with a potentially large number of policies. In this paper, we proposed an improved bit-vector algorithm named Condensate Bit Vector which can be adapted to large policy databases in the backbone network. Experiments showed that our proposed algorithm drastically improves in the storage requirements and search speed as compared to the original algorithm.

Given a graph G, a set of spanning trees of G are completely independent spanning trees (CISTs for short) if for any vertices x and y, the paths connecting them on these trees have neither vertex nor edge in common, except x and y. Hasunuma (2001, 2002) first introduced the concept of CISTs and conjectured that there are k CISTs in any 2k-connected graph. Later on, this conjecture was unfortunately disproved by Péterfalvi (2012). In this note, we show that Hasunuma's conjecture holds for graphs restricted in the class of 4-regular chordal rings CR(n,d), where both n and d are even integers.