Stanley M. Selkow

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Abstract. A straightforward linear time canonical labeling algorithm is shown to apply to almost all graphs (i .e. all but o(2 (2 >) of the 2 t 1 graphs on n vertices) . Hence, for almost all graphs X, any graph Y can be easily tested for isomorphism to X by an extremely naive linear time algorithm . This result is based on the following : In almost all(More)
A Hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v1, v2, . . . , vk of k distinct vertices of G, there exists a Hamiltonian cycle that encounters v1, v2, . . . , vk in this order. Define f(k, n) as the smallest integer m for which any graph on n vertices with minimum degree at least m is a k-ordered Hamiltonian graph. In this(More)
Imagine that you get such certain awesome experience and knowledge by only reading a book. How can? It seems to be greater when a book can be the best thing to discover. Books now will appear in printed and soft file collection. One of them is this book algorithms in a nutshell a desktop quick reference. It is so usual with the printed books. However, many(More)
A Gallai-coloring (G-coloring) is a generalization of 2-colorings of edges of complete graphs: a G-coloring of a complete graph is an edge coloring such that no triangle is colored with three distinct colors. Here we extend some results known earlier for 2-colorings to G-colorings. We prove that in every G-coloring of Kn there exists each of the following:(More)
A graph G on n vertices is called a Dirac graph if it has a minimum degree of at least n/2. The distance distG(u, v) is defined as the number of edges in a shortest path of G joining u and v. In this paper we show that in a Dirac graph G, for every small enough subset S of the vertices, we can distribute the vertices of S along a Hamiltonian cycle C of G in(More)
A number of examples are given where one seeks a minimal-cost tree to span a given subset of the nodes of a connected, directed, acyclic graph (we call such a graph monotonic). Some of these examples require an al~orithm to transform the problem into the form of a minimization problem in a monotonic graph.; this algorithm is also given. Finally, an implicit(More)
The typical problem in (generalized) Ramsey theory is to find the order of the largest monochromatic member of a family F (for example matchings, paths, cycles, connected subgraphs) that must be present in any edge coloring of a complete graph Kn with t colors. Another area is to find the minimum number of monochromatic members of F that partition or cover(More)
Improving a result of Sárközy and Selkow, we show that for all integers r, k ≥ 2 there exists a constant n0 = n0(r, k ) such that if n ≥ n0 and the edges of the complete graph Kn are colored with r colors then the vertex set of Kn can be partitioned into at most 100r log r + 2rk vertex disjoint connected monochromatic k-regular subgraphs and vertices. This(More)