Nowhere-zero unoriented flows in Hamiltonian graphs. (Q2810174)

An unoriented flow in a graph, is an assignment of real numbers to the edges, such that the sum of the values of all edges incident with each vertex is zero.NEWLINENEWLINE Let \(G\) be an undirected Hamiltonian graph. The authors obtained a bidirected graph by letting all edges of \(G\) to be extraverted. In the article, the authors observe that if the obtained graph has a nowhere-zero bidirected flow then it admits a nowhere-zero bidirected 12-flow. Equivalently, they show that if \(G\) has a nowhere-zero unoriented flow then it admits a nowhere-zero unoriented 12-flow. If \(G\) has certain special properties, stronger results are proved. In the second section some preliminaries on unoriented flows are discussed. In Section 3, they establish the claim for graphs with an odd number of vertices, and the final section consists of graphs with an even number of vertices. They prove that some conjecture is true for Hamiltonian graphs, with 6 replaced by 12.NEWLINENEWLINE The paper contains good results, it will be helpful to researchers working in the area of flows in Hamilitonian graphs.