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Six methods for implementing the widely used Clarke-Wright algorithm for the vehicle routing problem (VRP) are presented and compared. Fifty-five large test problems are used to compare the methods. The methods involve alternative ways to access adjacency information in both low and high density problems. The results clearly establish methods of choice for… (More)
A result of Ladas; Lakshmikantham, and Papadakis  concerning oscillation caused by lag in linear first order retarded argument differential equations is generalized to the sublinear case. Examples showing that such generalization to the superlinear case is impossible are given. 0. Introduction. It is known (, for example) that (A) g e C(R, R), g(t) <… (More)
A given nonincreasing sequence D = (d1, d2, · · · , dn) is said to contain a (nonincreasing) repetition sequence D∗ = (di1 , di2 , · · · , dik ) for some k ≤ n − 2 if all values of D −D∗ are distinct and for any dil ∈ D ∗ there exists some dt ∈ D −D∗ such that dil = dt. For any pair of integers n and k with n ≥ k + 2, we investigate the existence of a… (More)
For any natural number k, a graph G is said to be pancyclic mod k if it contains a cycle of every length modulo k. In this paper, we show that every K1,4-free graph G with minimum degree δ(G) ≥ k+ 3 is pancyclic mod k and every claw-free graph G with δ(G) ≥ k+ 1 is pancyclic mod k, which confirms Thomassen’s conjecture  for claw-free graphs.
In this paper, we investigate the sufficient conditions for a graph to contain a cycle (path) C such that G − V (C) is a disjoint union of cliques. In particular, sufficient conditions involving degree sum and neighborhood union are obtained.