Let X be a Polish space, that is, a separable, completely metrizable topological space. We always assume that X is non-empty and perfect, that is, X has no isolated points. An old theorem of Mycielski (see [8]) says that given a sequence of meager sets …Bn Í X k…n†: n < q†, where 1 < k…n† < q, there exists a perfect set P Í X such that P is free for each Bn , that is, P k…n† Ç Bn Í f…x0 ; . . ....

The standard solution concept for perfect-information extensive form games is subgame perfect Nash equilibrium. However, humans do not always play according to a subgame perfect Nash equilibrium, especially in games where it is possible for all the players to obtain much higher payoffs if they place some trust in each other (and this trust is not violated). In this paper, we introduce a new sol...

Let G = (V,E) be a graph and let S & V. The set S is a dominating set of G is every vertex of V-S is adjacent to a vertex of S. A vertex v of G is called S-perfect if \N[t~]nsi = 1 where N[v] denotes the closed neighborhood of v. The set S is defined to be a perfect neighborhood set of G if every vertex of G is S-perfect or adjacent with an S-perfect vertex. We prove that for all graphs G, O(G)...

We consider perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). In this paper, a generalized concatenation construction for q-ary 1-perfect codes is presented that allows us to construct q-ary 1-perfect codes of length (q − 1)nm + n +m from the given q-ary 1-perfect codes of length n = (q1 − 1)/(q − 1) and m = (q2 − 1)/(q − 1), where s1, s2 are ...

In a recent paper, perfect (n×n) space-time codes were introduced as the class of linear dispersion space-time codes having full rate, non-vanishing determinant, a signal constellation isomorphic to either the rectangular or hexagonal lattices in 2n dimensions and uniform average transmitted energy per antenna. Consequence of these conditions include optimality of perfect codes with respect to ...

In the leader election problem, n players wish to elect a random leader. The difficulty is that some coalition of players may conspire to elect one of its own members. We adopt the perfect information model: all communication is by broadcast, and the bad players have unlimited computational power. Protocols proceed in rounds: though players are synchronized between rounds, within each round the...

The enumeration of perfect matchings of graphs is equivalent to the dimer problem which has applications in statistical physics. A graph G is said to be n-rotation symmetric if the cyclic group of order n is a subgroup of the automorphism group of G. Jockusch (Perfect matchings and perfect squares, J. Combin. Theory Ser. A, 67(1994), 100-115) and Kuperberg (An exploration of the permanent-deter...

Let G $G$ be a graph on n $n$ vertices. For i ∈ { 0 , 1 } $i\in \{0,1\}$ spanning forest F $F$ of is called an $i$ -perfect if every tree in induced subgraph and exactly vertices have even degree (including zero). An proper it has no zero. Scott showed that connected with number contains (proper) 0-perfect forest. We prove one can find minimum edges polynomial time, but NP-hard to obtain maximu...