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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...

A graph is well covered if every maximal independent set has the same size and very well covered if every maximal independent set contains exactly half the number of vertices. In this paper, we present an alternative characterization of a certain sub-class of well-covered graphs and show that this generalizes a characterization of very well covered graphs given by Favaron 3].

In this paper we review the state of the art on graph privacy with special emphasis on applications to online social networks, and we consider some novel aspects which have not been greatly covered in the specialized literature on graph privacy. The following key considerations are covered: (i) choice of different operators to modify the graph; (ii) information loss based on the cost of graph o...

A graph G is a fractional ( , b k )-critical covered if − U [ ]-covered for every ⊆ V ) with | = which first defined by (Zhou, Xu and Sun, Inf. Process. Lett. 152 (2019) 105838). Furthermore, they derived degree condition to be graph. In this paper, we gain an independence number connectivity verify that ≥ max {2 +1)( +1)+4 bk +5/4 ,( +1) 2

A nontrivial connected graph is matching covered if each of its edges lies in a perfect matching. Two types of decompositions of matching covered graphs, namely ear decompositions and tight cut decompositions, have played key roles in the theory of these graphs. Any tight cut decomposition of a matching covered graph results in an essentially unique list of special matching covered graphs, call...

The inflation GI of a graph G with n(G) vertices and m(G) edges is obtained from G by replacing every vertex of degree d of G by a clique, which is isomorphic to the complete graph Kd, and each edge (xi, xj) of G is replaced by an edge (u, v) in such a way that u ∈ Xi, v ∈ Xj , and two different edges of G are replaced by non-adjacent edges of GI . The total domination number γt(G) of a graph G...

Six hens pecked a key (Experiment 1) or pushed a door (Experiment 2) to obtain food reinforcement. In both experiments and as an analogue of price changes, the response requirements were varied in two ways: by increasing the number of responses required and by increasing the required force of each response. The two price manipulations (response number and response force) had different effects o...