A graph G of order n is k-factor-critical, where k is an integer of the same parity as n with 0 ::; k ::; n, if G X has a perfect matching for any set X of k vertices of G. A k-factor-critical graph G is called minimal if for any edge e E E(G), G e is not k-factor-critical. In this paper we study some properties of minimally k-factor-critical graphs, in particular a bound on the minimum degree,...

Evolutionary game theory provides a fresh perspective on the prospects that agents with heterogeneous expectations might eventually come to agree on a single expectation. We establish conditions under which convergence of beliefs could occur, but also show that persistent heterogeneous expectations can arise if those conditions do not hold. The critical element is the degree of curvature in pay...

A graph G = (V, E) is called factor-critical if G = ∅ and G − v has a perfect matching for every vertex v ∈ V (G). A factor-critical graph G is tight (anti-tight, respectively) if for any v ∈ V (G), any perfect matching M in G − v, and any e ∈ M , |N (v) ∩ V (e)| = 1 (|N (v) ∩ V (e)| = 2, respectively), where N (v) denotes the neighborhood of v and V (e) denotes the set of vertices incident wit...

within the effective-field theory with correlations (eft), a transverse random field spin-1 ising model on the simple cubic (z=6) lattice is studied. the phase diagrams, the behavior of critical points, transverse magnetization,  internal energy, magnetic specific heat are obtained numerically and discussed for different values of p the concentration of the random transverse field.