Showing papers on "Path graph published in 1969"
TL;DR: A fast method is presented for finding a fundamental set of cycles for an undirected finite graph and is similar to that of Gotlieb and Corneil and superior to those of Welch and Welch.
Abstract: A fast method is presented for finding a fundamental set of cycles for an undirected finite graph. A spanning tree is grown and the vertices examined in turn, unexamined vertices being stored in a pushdown list to await examination. One stage in the process is to take the top element v of the pushdown list and examine it, i.e. inspect all those edges (v, z) of the graph for which z has not yet been examined. If z is already in the tree, a fundamental cycle is added; if not, the edge (v, z) is placed in the tree. There is exactly one such stage for each of the n vertices of the graph. For large n, the store required increases as n2 and the time as ng where g depends on the type of graph involved. g is bounded below by 2 and above by 3, and it is shown that both bounds are attained.In terms of storage our algorithm is similar to that of Gotlieb and Corneil and superior to that of Welch; in terms of speed it is similar to that of Welch and superior to that of Gotlieb and Corneil. Tests show our algorithm to be remarkably efficient (g = 2) on random graphs.
165 citations
01 Jan 1969
28 citations
TL;DR: In this paper, the same characterization was shown to hold for all n except for n = 4, where the existence of exactly one exceptional case is demonstrated. But this was only for cubic lattice graphs.
10 citations
TL;DR: In this paper, the complete graph with 2n+1 vertices was packed with copies of an arbitrary tree having n edges, which is a special case of the graph with n vertices.
Abstract: (1969). Can the Complete Graph with 2n+1 Vertices be Packed with Copies of an Arbitrary Tree having n Edges? The American Mathematical Monthly: Vol. 76, No. 10, pp. 1128-1130.
9 citations
TL;DR: A method of determining linear cyclic binary arrays, useful in generating binary patterns of finite length, is presented here.
Abstract: A method of determining linear cyclic binary arrays, useful in generating binary patterns of finite length, is presented here. The decimal number representation of the binary outputs of the pick-up heads are defined as states of the system. A state graph showing these states as vertices and ares corresponding to transitions from one state to another is developed. Determination of an array is equivalent to the realization of a circuit in this state graph connecting all the vertices and traversing no vertex or arc twice.