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the chromatic number of a graph g, denoted by χ(g), is the minimum number of colors such that g can be colored with these colors in such a way that no two adjacent vertices have the same color. a clique in a graph is a set of mutually adjacent vertices. the maximum size of a clique in a graph g is called the clique number of g. the turán graph tn(k) is a complete k-partite graph whose partition...

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Over the past three years, a wrist-type golf-score counter has been found helpful in recording movement rates for behavior modification and analysis. Several different types are available from local sporting goods stores. The most cosmetic and reliable model located to date is the "Domatic Score", which is manufactured in Switzerland and can be obtained from the Hoffritz Cutlery Company, 49 Eas...

a positive integer $n$ is called a clt number if every group of order $n$ satisfies the converse of lagrange's theorem. in this note, we find all clt and supersolvable numbers up to $1000$. we also formulate some questions about the distribution of these numbers.

the zarankiewicz number z(b; s) is the maximum size of a subgraph of kb,b which does not contain ks,s as a subgraph. the two-color bipartite ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of kb,b with two colors contains a ks,s in the rst color or a kt,t in the second color.in this work, we design and exploit a computational method for bounding and computin...