The stability number of the graph G, denoted by α(G), is the cardinality of a maximum stable set of G. In this paper we characterize the square-stable graphs, i.e., the graphs enjoying the property α(G) = α(G), where G is the graph with the same vertex set as in G, and an edge of G is joining two distinct vertices, whenever the distance between them in G is at most 2. We show that every square-...

‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...

. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . Commentary . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ....

In 1987, Lovv asz conjectured that every brick G diierent from K 4 , C 6 , and the Petersen graph has an edge e such that G e is a matching covered graph with exactly one brick. Lovv asz and Vempala announced a proof of this conjecture in 1994. Their paper is under preparation. We present here an independent proof of their theorem. We shall in fact prove that if G is any brick diierent from K 4...

We conducted preference assessments with 4 typically developing children to identify potential reinforcers and assessed the reinforcing efficacy of those stimuli. Next, we tested two predictions of economic theory: that overall consumption (reinforcers obtained) would decrease as the unit price (response requirement per reinforcer) increased and that the cost and benefit components that defined...