Guess-and-determine attack is one of the general attacks on stream ciphers. It is a common cryptanalysis tool for evaluating security of stream ciphers. The effectiveness of this attack is based on the number of unknown bits which will be guessed by the attacker to break the cryptosystem. In this work, we present a relation between the minimum numbers of the guessed bits and uniquely restricted...

We describe an exact algorithm for the problem of sorting a permutation by the minimum number of reversals, originating from evolutionary studies in molecular biology. Our approach is based on an integer linear programming formulation of a graph-theoretic relaxation of the problem, calling for a decomposition of the edge set of a bicolored graph into the maximum number of alternating cycles. Th...

A conjecture of the first two authors is that $n$ matchings size in any graph have a rainbow matching $n-1$. We prove lower bound $\frac{2}{3}n-1$, improving on trivial $\frac{1}{2}n$, and an analogous result for hypergraphs. For $\{C_3,C_5\}$-free graphs disjoint we obtain $\frac{3n}{4}-O(1)$. also discuss alternating paths, if true would yield $n-\sqrt{2n}$. non-alternating (ordinary paths) v...

A fullerene graph F is a cubic 3-connected plane graph with exact 12 pentagons and other hexagons. Let M be a perfect matching of F . A cycle C of F is M -alternating if and only if the edges of C appear alternately in and off M . A set H of disjoint hexagons of F is called a resonant pattern if F has a perfect matching M such that all hexagons in H are M -alternating. A fullerene graph F is k-...

a special class of cubic graphs are the cycle permutation graphs. a cycle permutation graph pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.in this paper we determine a good upper bound for tenacity of cycle permutation graphs.

Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of matchings via alternating cycles. Namely, want to find a sequence which transforms one given another such that symmetric difference each pair consecutive is single cycle. The equivalent combinatorial path polytopes. We prove NP-hard even when graph planar or bipartite, but it can be solved pol...

For an undirected graph and a fixed integer k, a 2-matching is said to be Ck-free if it has no cycle of length k or less. In particular, a C4-free 2-matching in a bipartite graph is called a square-free 2-matching. The problem of finding a maximum Ck-free 2-matching in a bipartite graph is NP-hard when k ≥ 6, and polynomially solvable when k = 4. Also, the problem of finding a maximum-weight Ck...

In this paper, we continue the study of the domination game in graphs introduced by Bre{v{s}}ar, Klav{v{z}}ar, and Rall. We study the paired-domination version of the domination game which adds a matching dimension to the game. This game is played on a graph $G$ by two players, named Dominator and Pairer. They alternately take turns choosing vertices of $G$ such that each vertex chosen by Domin...

A connected graph is said to be k-cycle resonant if, for 16 t6 k, any t disjoint cycles in G are mutually resonant, that is, there is a perfect matching M of G such that each of the t cycles is an M -alternating cycle. The concept of k-cycle resonant graphs was introduced by the present authors in 1994. Some necessary and su6cient conditions for a graph to be k-cycle resonant were also given. I...

The alternating group graph, which belongs to the class of Cayley graphs, is one of the most versatile interconnection networks for parallel and distributed computing. In this paper, adopting the conditional fault model in which each vertex is assumed to be incident with two or more fault-free edges, we show that an n-dimensional alternating group graph can tolerate up to 4n − 13 edge faults, w...