paths and cyclesThe function f ( n ) is defined to be the smallest integer such that any f ( n )-chromatic digraph contains all paths with two blocks P ( k , j ) with k + j = n - 1. El Sahili conjectured that f
A few tries will tell you no; that graph does not have an Euler circuit. When we were working with shortest paths, we were interested in the optimal path. With Euler paths and circuits, we’re primarily interested in whether an Euler path or circuitexists. Why do we care if an Euler ...
Keywords Tournaments Antidirected Hamiltonian paths Hamiltonian circuits 1. Introduction The study of Hamiltonian paths and cycles in tournaments is a classic field of investigation in graph theory, and a classic topic is the existence and the parity of the number of oriented paths and cycles in tou...
, Graph Theory, Combinatorics, and Applications: Proceedings of the Seventh Quadrennial International Conference on the Theory and Applications of Graphs, vol. 1, Wiley, New York (1995), pp. 251-263 Google Scholar [27] S.J. Curran, Hamilton circuits in Cayley digraphs on abelian groups and ...
The mathematical models of Euler circuits and Euler paths can be used to solve real-world problems. Learn about Euler paths and Euler circuits, then practice using them to solve three real-world practical problems. Euler Paths and Circuits In this video lesson, we are going to see how Euler...
Fleury’s algorithm is a precise and reliable method for determining whether a given graph contains Eulerian paths, circuits, or none at all. By following a series of steps, this algorithm methodically explores the graph, keeping track of the visited edges and, in the process, unveils the Eule...
This paper extends the classical notion of critical paths in combinational circuits to the case of synchronous circuits that use level-sensitive latches. Critical paths in such circuits arise from setup, hold, and cyclic constraints on the data signals at the inputs of each latch and may extend...
Counting hamiltonian circuits on a grid is quite different from problems which was viewed there. In article I view foremost masks over subsets and paths in graphs. But in your problem motzkin words and matrix multiplication are used:)Maybe I will view your problem in fiture article:) → Reply...
In many animals, neuronal circuits are dedicated to analyse the temporal pattern of sensory stimuli that instruct the klinotactic response. Moreover, neuronal circuits are composed of 'on' and 'off cells' that register the ups and downs of sensory stimuli. Temporal sampling during klinotaxis is...
In this paper, we are interested in a generalization to hypergraphs of the extremal theory of paths and cycles in graphs. Following Berge [1], a k-cycle is a set system {Ai:i∈Zk} such that the family {Ai∩Ai+1:i∈Zk} has a system of distinct representatives. It is convenient to...