We study the constructive variant of the control problem for Condorcet voting, where control is done by deleting voters. We prove that this problem remains NP-hard for the Condorcet-consistent voting rule Uncovered Alternatives. Furthermore, we develop a relation-algebraic model of Condorcet voting and relation-algebraic specifications of the dominance relation and the solutions of the control ...

Let k be a positive integer. A vertex subset D of a graph G = (V,E) is a perfect k-dominating set of G if every vertex v of G, not in D, is adjacent to exactly k vertices of D. The minimum cardinality of a perfect k-dominating set of G is the perfect k-domination number γkp(G). In this paper, we generalize perfect domination to perfect k-domination, where many bounds of γkp(G) are obtained. We ...

The study of non-orientable matroids has not received very much attention compared with the study of representable matroids or oriented matroids. Proving non-orientability of a matroid is known to be a difficult problem even for small matroids of rank 3. RichterGebert [4] even proved that this problem is NP-complete. In general, there are only some necessary conditions (Proposition 6.6.1 of [1]).

We investigate the problem of finding a total order of a finite set that satisfies various local ordering constraints. Depending on the admitted constraints, we provide an efficient algorithm or prove NP-completeness. We discuss several generalisations and systematically classify the problems.

In southern India, there are traditional patterns of line-drawings encircling dots, called “Kolam”, among which one-line drawings or the “infinite Kolam” provide very interesting questions in mathematics. For example, we address the following simple question: how many patterns of infinite Kolam can we draw for a given grid pattern of dots? The simplest way is to draw possible patterns of Kolam ...

In this paper, we consider multicriteria and cardinality constrained multicut problems. Let G be a graph where each edge is weighted by R positive costs corresponding to R criteria and consider k source-sink pairs of vertices of G and R integers B1, . . . , BR. The problem R-CriMultiCut consists in finding a set of edges whose removal leaves no path between the ith source and the ith sink for e...

Suguru is a paper and pencil puzzle invented by Naoki Inaba. The goal of the game to fill grid with numbers between 1 5 while respecting three simple constraints. We first prove NP-completeness puzzle. For this we design gadgets encode PLANAR-CIRCUIT-SAT in grid. then physical Zero-Knowledge Proof (ZKP) protocol for Suguru. This ZKP allows prover that he knows solution verifier without leaking ...