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New Construction Techniques for H2(8t,3)s

Dinesh G. Sarvate1, Li Zhang2
1Department of Mathematics College of Charleston Charleston, SC 29424 The Citadel
2 Department of Mathematics and Computer Science The Citadel Charleston, SC 29424

Abstract

An H2 graph is a multigraph on three vertices with a double edge between one pair of distinct vertices and a single edge between the other two pairs. The problem of decomposing a complete multigraph 3K8t into H2 graphs has been completely solved. In this paper, we describe some new procedures for such decompositions and pose the following question: Can these procedures be adapted or extended to provide a unified proof of the existence of H2(8t,λ)’s?