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In previous papers, Catlin introduced four functions, denoted S O , S R , S C , and S H , between sets of ÿnite graphs. These functions proved to be very useful in establishing properties of several classes of graphs, including supereulerian graphs and graphs with nowhere zero k-ows for a ÿxed integer k ¿ 3. Unfortunately, a subtle error caused several… (More)

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Keywords: Balanced graphs 1-balanced graphs Cartesian product of graphs Web graphs a b… (More)

In this paper we prove that if k is an integer no less than 3, and if G is a two-connected graph with 2n-a vertices, a E {0, 1}, which is regular of degree n-k, then G is Hamiltonian if a = 0 and n > k 2 + k + 1 or if a = I and n > 2k 2-3k =, 3. We use the notation and terminology of [1]. Gordon [4] has proved that there are only a small number of… (More)