Leaves for packings with block size four

期刊： AUSTRALASIAN JOURNAL OF COMBINATORICS, 2021; 80 ()

We consider maximum packings of edge-disjoint 4-cliques in the complete graph K-n. When n equivalent to 1 or 4 (mod 12), these are simply block design......

On the construction of weighing matrices using negacyclic matrices

期刊： AUSTRALASIAN JOURNAL OF COMBINATORICS, 2021; 80 ()

We construct weighing matrices by 2-suitable negacyclic matrices, and study the conjecture by J. S. Wallis in 1972 that "For every n equivalent to 2 (......

Gallai-Ramsey numbers of C-10 and C-12

期刊： AUSTRALASIAN JOURNAL OF COMBINATORICS, 2021; 79 ()

A Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles, and a Gallai k-coloring is a Gallai coloring that uses at ......

A note on strong edge choosability of toroidal subcubic graphs

期刊： AUSTRALASIAN JOURNAL OF COMBINATORICS, 2021; 79 ()

Let G be a graph. A proper edge-coloring of G is called a strong edge-coloring if any two edges on a path of length at most three receive distinct col......