Deciding 3-colorability for general plane graphs is known to be an NP-complete problem. 31 However, for certain families of graphs, like triangulations, polynomial time algorithms 32 exist. We consider the family of pseudo-triangulations, which are a generalization of 33 triangulations, and prove NP-completeness for this class. This result also holds if we 34 bound their face degree to four, or...

Representation of the algebra of FP (anti)ghosts in string theory is studied by generalizing the recursive fermion system in the Cuntz algebra constructed previously. For that purpose, the pseudo Cuntz algebra, which is a ∗-algebra generalizing the Cuntz algebra and acting on indefinite-metric vector spaces, is introduced. The algebra of FP (anti)ghosts in string theory is embedded into the pse...

Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras. Their properties and connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. In this paper we study the class of perfect pseudo-BCK algebras with pseudo-product and we prove that any perfect pseudo-BCK algebra with pseudo-product is strongly bipartite. Anothe...

For set functors preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. And the initial algebra consists of all well-pointed coalgebras that are well-founded in the sense of Osius [20] and Taylor [27]. Finally, ...

A normal pseudo-BCK-algebra X is an algebra in which every subalgebra of X is an ideal of X . Characterizations of normal pseudo-BCK-algebras are given. 2010 Mathematics Subject Classification: 03G25, 06F35.

All −1-type pointed Hopf algebras with Weyl groups of exceptional type are found. It is proved that every non −1-type pointed Hopf algebra is infinite dimensional. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Weyl group.