On representable pairs

Representable Disjoint NP-Pairs

Classes of Representable Disjoint NP - Pairs 1

For a propositional proof system P we introduce the complexity class DNPP(P ) of all disjoint NP-pairs for which the disjointness of the pair is efficiently provable in the proof system P . We exhibit structural properties of proof systems which make canonical NP-pairs associated with these proof systems hard or complete for DNPP(P ). Moreover, we demonstrate that non-equivalent proof systems c...

Classes of representable disjoint NP-pairs

For a propositional proof system P we introduce the complexity class DNPP(P) of all disjoint NP-pairs for which the disjointness of the pair is efficiently provable in the proof system P . We exhibit structural properties of proof systems which make canonical NP-pairs associated with these proof systems hard or complete for DNPP(P). Moreover, we demonstrate that nonequivalent proof systems can ...

On 132-representable graphs

A graphG = (V,E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if xy is an edge in E. Word-representable graphs are the main focus in “Words and Graphs” by Kitaev and Lozin. A word w = w1 · · ·wn avoids the pattern 132 if there are no 1 ≤ i1 < i2 < i3 ≤ n such that wi1 < wi3 < wi2. A recently suggested research direction ...

On Representable Graphs

A graph G = (V,E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) ∈ E for each x 6= y. If W is k-uniform (each letter of W occurs exactly k times in it) then G is called k-representable. Examples of non-representable graphs are found in this paper. Some wide classes of graphs are proven to be 2and 3-representable. Seve...