We generalize the well-known theorem of Corrádi and Hajnal which says that if a given graph G has at least 3k vertices and the minimum degree of G is at least 2k, then G contains k vertex-disjoint cycles. Our main result is the following; for any integer k, there is an absolute constant ck satisfying the following; let G be a graph with at least ck vertices such that the minimum degree of G is ...

Cyclic m-cycle systems of order v are constructed for all m ≥ 3, and all v ≡ 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for the existence of a cyclic m-cycle syst...

In 6] Misra introduced the powerlist notation and used it to succintly describe several parallel algorithms. In particular, algorithms that use a balanced divide and conquer strategy have elegant descriptions as powerlist functions. Among the examples presented were two sorting networks due to Batcher 1]. To prove their correctness a-posteriori, Misra used the 0-1 principle, which states that a...

‎let $g$ be a graph with vertex set $v(g)$ and edge set $x(g)$ and consider the set $a={0,1}$‎. ‎a mapping $l:v(g)longrightarrow a$ is called binary vertex labeling of $g$ and $l(v)$ is called the label of the vertex $v$ under $l$‎. ‎in this paper we introduce a new kind of graph energy for the binary labeled graph‎, ‎the labeled graph energy $e_{l}(g)$‎. ‎it depends on the underlying graph $g$...

In this paper, we study a new coloring parameter of graphs called the gap vertexdistinguishing edge coloring. It consists in an edge-coloring of a graph G which induces a vertex distinguishing labeling of G such that the label of each vertex is given by the difference between the highest and the lowest colors of its adjacent edges. The minimum number of colors required for a gap vertex-distingu...

In this paper we examine the average running times of Batcher's bitonic merge and Batcher's odd-even merge when they are used as parallel merging algorithms. It has been shown previously that the running time of odd-even merge can be upper bounded by a function of the maximal rank diierence for elements in the two input sequences. Here we give an almost matching lower bound for odd-even merge a...

This paper presents sorting network based architectures for computing non-recursive and recursive median lters. The proposed architectures are highly pipelined, and consist of fewer compare-swap units than existing architectures. The reduction in the number of compare-swap units is achieved by minimizing computational overlap between successive outputs, and also by using Batcher's odd-even merg...