We investigate the complexity of a puzzle that turns out to be NLcomplete.

The achromatic number of a nite graph G, (G), is the maximum number of independent sets into which the vertex set may be partitioned, so that between any two parts there is at least one edge. For an m-dimensional hypercube P m 2 we prove: There exist constants 0 < c 1 < c 2 , independent of m, such that

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (clo...

Why are n-player games much more complex than two-player games? Is it much more difficult to cooperate or to compete? n-player Toppling Dominoes is an n-player version of Toppling Dominoes, a two-player combinatorial game. Because of queer games, i.e., games where no player has a winning strategy, cooperation is a key-factor in nplayer games and, as a consequence, n-player Toppling Dominoes pla...

We show that the problem of counting the number of Eulerian circuits in an undirected graph is complete for the class #P. The method employed is mod-p reduction from counting Eulerian orientations.

The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...