Generating Constrained Lattice Paths in a Grid Related to Counting Cycles

Abstract

This paper gives a bijection between two classes of lattice paths in an n × n grid. This bijection is crucial for identifying short cycles in simple bipartite graphs. We also give an algorithm for generating such paths with the complexity of O (4n/n1/2). The proposed work lays the groundwork for counting cycles of length from g to 2g - 2 in bipartite graphs, where g is the girth of the graph. which has broader implications on Error correcting codes, cryptography etc. © 2025 Elsevier B.V., All rights reserved.