We present a simple family of Bell inequalities applicable to a scenario involving arbitrarily many parties, each of which performs two binary-outcome measurements. We show that these inequalities are members of the complete set of full-correlation Bell inequalities discovered by Werner-Wolf-Żukowski-Brukner. For scenarios involving a small number of parties, we further verify that these inequa...

The list Ramsey number R ℓ ( H , k ) ${R}_{\ell }(H,k)$ recently introduced by Alon, Bucić, Kalvari, Kuperwasser, and Szabó, is a list-coloring variant of the classical number. They showed that if $H$ fixed r $r$ -uniform hypergraph not -partite colors $k$ goes to infinity, e Ω ≤ O ${e}^{{\rm{\Omega }}(\sqrt{k})}\le {R}_{\ell }(H,k)\le {e}^{O(k)}$ . We prove = Θ }(H,k)={e}^{{\rm{\Theta }}(k)}$ ...

An outerplanar (also called circular, convex, one-page) drawing of an n-vertex graph G is a drawing in which the vertices are placed on a circle and each edge is drawn using one straight-line segment. We derive exact results for the minimal number of crossings in any outerplanar drawings of the following classes of graphs: 3-row meshes, Halin graphs and complete p−partite graphs with equal size...

L. Volkmann, Discrete Math. 245 (2002) 19-53 posed the following question. Let 4 ≤ m ≤ n. Are there strong n-partite tournaments, which are not themselves tournaments, with exactly n − m + 1 cycles of length m? We answer this question in affirmative. We raise the following problem. Given m ∈ {3, 4, . . . , n}, find a characterization of strong n-partite tournaments having exactly n −m + 1 cycle...

The vertex set of a digraph D is denoted by V (D). A c-partite tournament is an orientation of a complete c-partite graph. A digraph D is called cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (D) = V (C1) ∪ V (C2), and a multipartite tournament D is called weakly cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (C1) ∪ V (C2...

A bipartite graph is hamiltonian laceable if there exists a hamiltonian path between any two vertices that are in different partite sets. A hamiltonian laceable graph G is said to be hyperhamiltonian laceable if, for any vertex v of G, there exists a hamiltonian path of G−{v} joining any two vertices that are located in the same partite set different from that of v. In this paper, we further im...

Moon [J. Combin. Inform. System Sci. 19 (1994), 207–214] showed that every strong tournament contains a Hamiltonian cycle through at least three pancyclic arcs. In this paper, we extend the result of Moon and prove that if D is a strong c-partite tournament with c ≥ 3, then D contains a cycle C containing vertices from exactly c partite sets such that C contains at least three arcs, each of whi...