The $H$-matching problem asks to partition the vertices of an input graph $G$
into sets of size $k=|V(H)|$, each of which induces a subgraph of $G$
isomorphic to $H$. The $H$-matching problem has been classified as polynomial
or NP-complete depending on whether $k\leq 2$ or not. We consider a variant
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Barnette's conjecture is the statement that every 3-connected cubic
planar bipartite graph is Hamiltonian. Goodey showed that the conjecture
holds when all faces of the graph have either 4 or 6 sides. We
generalize Goodey's result by showing that when the faces of such a
graph are 3-colored, with adjacent ... more >>>

We formulate a formal syntax of approximate formulas for the logic with counting
quantifiers, $\mathcal{SOLP}$, studied by us in \cite{aaco06}, where we showed the
following facts:
$(i)$ In the presence of a built--in (linear) order, $\mathcal{SOLP}$ can
describe {\bf NP}--complete problems and fragments of it capture classes like
{\bf P} ... more >>>