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45  Articles
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In this paper we improve the upper bound on the multi-color Ramsey numbers of paths and even cycles. More precisely, we prove the following. For every r=2r\geq 2 there exists an n0=n0(r)n_0=n_0(r) such that for n=n0n\geq n_0 we have Rr... see more

The edge-distinguishing chromatic number (EDCN) of a graph G is the minimum positive integer k such that there exists a vertex coloring c : V(G)?{1, 2, …, k} whose induced edge labels {c(u),c(v)} are distinct for al... see more

Graph embedding is a powerful method in parallel computing that maps a guest network G into a host network H. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion, and the wirelength. In th... see more

In this paper, we first coin a new graph theoretic problem called the diameter cycle problem with numerous applications. A longest cycle in a graph G = (V, E) is referred to as a diameter cycle of G iff the distance in G of every vertex on ... see more

This is a survey of results obtained during the last 45 years regarding the intersection behaviour of all longest paths, or all longest cycles, in connected graphs. Planar graphs and graphs of higher connectivity receive special attention. Graphs embeddab... see more

A dynamic programming method for enumerating hamiltonian cycles in arbitrary graphs is presented. The method is applied to grid graphs, king's graphs, triangular grids, and three-dimensional grid graphs, and results are obtained for larger cases than prev... see more

Let R = S/I where S = k[T_1, . . . , T_n] and I is a homogeneous ideal in S. The acyclic closure R<Y> of k over R is a DG algebra resolution obtained by means of Tate’s process of adjoining variables to kill cycles. In a similar way one can obtain t... see more

Let R = S/I where S = k[T_1, . . . , T_n] and I is a homogeneous ideal in S. The acyclic closure R<Y> of k over R is a DG algebra resolution obtained by means of Tate’s process of adjoining variables to kill cycles. In a similar way one can obtain t... see more


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