(V,A, c) be a directed network with node set V , arc set A = {e1, · · · , em}, and capacities on arcs c : A 7→ R+, where R+ is the set of non-negative rational numbers. Let s, t ∈ V be two distinct nodes, designated as the source and the destination. Let P = {p1, · · · , pk} be the set of s-t paths in G. Let aij = 1 if arc ei ∈ A lies on path pj ∈ P and aij = 0 otherwise. Let f : P 7→ R+ be a f...

CRYAA plays critical functional roles in lens transparency and opacity, and polymorphisms near CRYAA have been associated with age-related cataract (ARC). This study examines polymorphisms in the CRYAA promoter region for association with ARC and elucidates the mechanisms of this association. Three SNPs nominally associated with ARC were identified in the promoter region of CRYAA: rs3761382 (P ...

This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonian-connected graphs and digraphs.

Jackson and Ordaz conjectured that if the stability number (G) of a graph G is no greater than its connectivity (G) then G is pancyclic. Applying Ramsey’s theorem we prove the pancyclicity of every graph G with (G) su7ciently large with respect to (G). c © 2003 Elsevier B.V. All rights reserved. MSC: 05C38; 05C45

In this note, we consider the i-block intersection graphs (i-BIG) of a universal-friend friendship 3-hypergraph and show that they are pancyclic for i = 1, 2. We also show that the 1-BIG of a universalfriend friendship 3-hypergraph is Hamiltonian-connected.

We present a fast local search algorithm that finds an improved solution (if there is any) in the k-exchange neighborhood of the given solution to an instance of WEIGHTED FEEDBACK ARC SET IN TOURNAMENTS. More precisely, given an arc weighted tournament T on n vertices and a feedback arc set F (a set of arcs whose deletion from T turns it into a directed acyclic graph), our algorithm decides in ...

We present a fast local search algorithm that finds an improved solution (if there is any) in the k-exchange neighborhood of the given solution to an instance of WEIGHTED FEEDBACK ARC SET IN TOURNAMENTS. More precisely, given an arc weighted tournament T on n vertices and a feedback arc set F (a set of arcs whose deletion from T turns it into a directed acyclic graph), our algorithm decides in ...