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Thomassen conjectured that every longest circuit of a 3-connected graph has a chord. It is proved in this paper that every longest circuit of a 4-connected graph embedded in a torus or Klein bottle has a chord.

Thomassen conjectured that every longest circuit of a 3-connected graph has a chord. The conjecture is veriÿed in this paper for projective planar graphs with minimum degree at least 4.

OpenACC provides a high-productivity API for programming GPUs and similar accelerator devices. One of the last steps in tuning OpenACC programs is selecting values for the num_gangs and vector_length clauses, which control how a parallel workload is distributed to an accelerator's processing units. In this paper, we present OptACC, an autotuner that can… (More)

Let k ≥ 2 be an integer and G a 2-connected graph of order |G| ≥ 3 with minimum degree at least k. Suppose that |G| ≥ 8k − 16 for even |G| and |G| ≥ 6k − 13 for odd |G|. We prove that G has a [k, k + 1]-factor containing a given Hamiltonian cycle if max{deg G (x), deg G (y)} ≥ |G|/2 for each pair of nonadjacent vertices x and y in G. This is best possible… (More)