It is a well-known conjecture that if a regular graph G of order 2n has degree d(G) satisfying d(G) ^ n, then G is the union of edge-disjoint 1-factors. It is well known that this conjecture is true for d(G) equal to 2n —1 or 2n — 2. We show here that it is true for d(G) equal to2n — 3, In — 4, or2n — 5. We also show that it is true for </(G)>$|K(G)|.
1. Introduction The graphs we consider here are either simple graphs, that is they have no loops or multiple edges, or are multigraphs, that is they may have more than one edge joining a pair of vertices, but again have no loops. In particular we shall consider a special kind of multigraph, called a star-multigraph: this is a multigraph which contains a… (More)
Inhibition is a central construct to the frontal lobe theory of ageing, yet its construct validity remains unproven. Furthermore, age effects on measures of inhibition are often reported without adequate control for the effects of global slowing on performance. We investigated inhibitory function in older adults in two experiments. In Experiment 1, 49… (More)