Compatible Spanning Circuits Visiting Each Vertex Exactly a Specified Number of Times in Graphs with Generalized Transition Systems - Guo, Zhiwei; Chen, Xiaoxia (Parallel processing letters, 2024)
A transition in a graph refers to a pair of adjacent edges. A generalized transition system F ( G ) over a graph G , which can be regarded as a generalization of a partition system or an edge-coloring of G , defines a set of transitions over G . A compatible spanning circuit in a graph G with a generalized transition system F ( G ) refers to a spanning circuit in which no two consecutive edges form a transition defined by F ( G ) . In this paper, we present sufficient conditions for the existence of compatible spanning circuits that visit each vertex exactly k times in some specific graphs on n ≥ f ( k ) vertices with generalized transition systems, where f ( k ) denotes a function of a positive integer k , for every feasible k . Moreover, as corollaries, we also obtain analogous conclusions for the above mentioned graphs that are assigned partition systems and edge-colorings, respectively.