A graph G is a Zm-well-covered graph if |I1| ≡ |I2| (modm) for all maximal independent sets I1 and I2 in V (G) [3]. The recognition problem of Zm-well-covered graphs is a Co-NP-Complete problem. We give a characterization of Zm-well-covered graphs for chordal, simplicial and circular arc graphs. c © 2001 Elsevier Science B.V. All rights reserved.

We study the computational complexity of packing puzzles of identical polyominoes. Packing dominoes (i.e., 1 × 2 rectangles) into grid polygons can be solved in polynomial time by reducing to a bipartite matching problem. On the other hand, packing 2 × 2 squares is known to be NP-complete. In this paper, we fill the gap between dominoes and 2 × 2 squares, that is, we consider the packing puzzle...

Buttons & Scissors is a popular single-player puzzle. A level is played on an n-by-n grid, where each position is empty or has a single coloured button sewn onto it. The player’s goal is to remove all of the buttons using a sequence of horizontal, vertical, and diagonal scissor cuts. Each cut removes all buttons between two distinct buttons of the same colour, and is not valid if there is an in...

We show that the problem of deciding whether a digraph has a Hamiltonian path between two specified vertices and the problem of deciding whether a given graph has a cubic subgraph are complete for monotone NP via monotone projection translations. We also show that the problem of deciding whether a uniquely partially orderable (resp. comparability) graph has a cubic subgraph is complete for NP v...

In this paper we show that the problem to decide whether the hamiltonian index of a given graph is less or equal to a given constant is Research supported by grants No. 1M0545 and MSM 4977751301 of the Czech Ministry of Education. Supported by Nature Science Funds of China under Contract Grant No.: 10671014

The logic of context with the ist (c;p) modality has been proposed by McCarthy as a foundation for con-textual reasoning. This paper shows that proposi-tional logic of context is NP-complete and therefore more tractable than multimodal logics or Multi Language hierarchical logics which are PSPACE-complete. This result is given in a proof-theoretical way by providing a tableau calculus, which ca...

Solitaire Chess” is a logic puzzle published by ThinkfunTM that can be seen as a single person version of traditional chess. Given a chess board with some chess pieces of the same color placed on it, the task is to capture all pieces but one using only moves that are allowed in chess. Moreover, in each move one piece has to be captured. We prove that deciding if a given instance of Solitaire Ch...

Two Dots is a popular single-player puzzle video game for iOS and Android. In its simplest form, the game consists of a board with dots of different colors, and a valid move consists of connecting a sequence of adjacent dots of the same color. We say that dots engaged in a move are “hit” by the player. After every move, the connected dots disappear, and the void is filled by new dots (the entir...

I investigate the problem of contracting a dependency-network with respect to any of its nodes. The resulting contraction must not contain the node in question, but must also be a minimal mutilation of the original network. Identifying successful and minimally mutilating contractions of dependencynetworks is non-trivial, especially when non-well-founded networks are to be taken into account. I ...

Clique-width is a graph parameter that measures in a certain sense the complexity of a graph. Hard graph problems (e.g., problems expressible in Monadic Second Order Logic with second-order quantification on vertex sets, that includes NP-hard problems such as 3-colorability) can be solved in polynomial time for graphs of bounded clique-width. We show that the clique-width of a given graph canno...