Quadratic leaves of maximal partial triple systems
The authors prove that every graph having vertex degrees zero and two, an odd number of vertices, number of edges congruent to v(v-1)/2 mod 3, and no triangles, is the leave of a maximal partial triple system. The only exception to this result is the union of a four cycle and a five cycle on nine vertices. The proof is by direct construction, using difference techniques and the results of Simpson on the existence of Langford sequences. Many cases have to be considered due to the direct nature of the proof, but the authors have done a fine job of unifying cases without detracting from the clarity of the exposition.
scientific article; zbMATH DE number 3985226
scientific article