22,519 research outputs found
Cycles in Random Bipartite Graphs
In this paper we study cycles in random bipartite graph . We prove
that if , then a.a.s. satisfies the following. Every
subgraph with more than edges contains a
cycle of length for all even . Our theorem
complements a previous result on bipancyclicity, and is closely related to a
recent work of Lee and Samotij.Comment: 8 pages, 2 figure
A Message-Passing Algorithm for Counting Short Cycles in a Graph
A message-passing algorithm for counting short cycles in a graph is
presented. For bipartite graphs, which are of particular interest in coding,
the algorithm is capable of counting cycles of length g, g +2,..., 2g - 2,
where g is the girth of the graph. For a general (non-bipartite) graph, cycles
of length g; g + 1, ..., 2g - 1 can be counted. The algorithm is based on
performing integer additions and subtractions in the nodes of the graph and
passing extrinsic messages to adjacent nodes. The complexity of the proposed
algorithm grows as , where is the number of edges in the
graph. For sparse graphs, the proposed algorithm significantly outperforms the
existing algorithms in terms of computational complexity and memory
requirements.Comment: Submitted to IEEE Trans. Inform. Theory, April 21, 2010
- β¦