For a fixed pattern graph H , let H -Contractibility denote the problem of deciding whether a given input graph is contractible to H . This paper is part I of our study on the computational complexity of the H -Contractibility problem. We continue a line of research that was started in 1987 by Brouwer and Veldman, and we determine the computational complexity of the H -Contractibility problem f...

Let and be randomly chosen subsets of the first positive integers cardinalities , such that their sumset has size . We show asymptotically almost surely are fully contained in arithmetic progressions with same common difference approximately also prove a counting theorem for pairs sets arbitrary abelian groups. The results hold Our main tool is an asymmetric version method hypergraph containers...

Arabic character recognition of handwriting is addressed. A novel approach for the Arabic Character Recognition is presented based on statistical analysis of a typical Arabic text is presented. Results showed that the sub-word in Arabic language is the basic pictorial block rather than the word. The method of approximate stroke sequence is applied for the recognition of some Arabic characters i...

For a fixed pattern graph H, let H-CONTRACTIBILITY denote the problem of decidingwhether a given input graph is contractible to H. We continue a line of research that wasstarted in 1987 by Brouwer & Veldman, and we determine the computational complexity ofH-CONTRACTIBILITY for certain classes of pattern graphs. In particular, we pin-pointthe complexity for all graphs H with five...