The modulo orientation problem seeks a so-called mod -orientation of an undirected graph, in which the indegree is equal to outdegree under modulo at each ...

In this paper, we prove a relatively positive result that if a graph family has a bounded matching number, then after cer- tain reduction operations, there are ...

Jul 1, 2022 · The modulo orientation problem seeks a so-called mod ( 2 t + 1 )-orientation of an undirected graph, in which the indegree is equal to ...

In this paper, we study the flip graph on the perfect matchings of a complete graph of even order. We investigate its combinatorial and spectral properties ...

Jul 1, 2022 · The modulo orientation problem seeks a so-called mod ( 2 t + 1 ) -orientation of an undirected graph, in which the indegree is equal to ...

Dec 16, 2022 · In particular, when b = 0, any b-orientation is a mod k-orientation of G. The studies of group connectivity and modulo orientation of graphs are ...

Dividing this product by the total number of matchings provides an estimate of the second-moment, which is the expected number of pairs of valid orientations.

In Chapter 3, we show that there are essentially finite many exceptions for graphs with bounded matching numbers not admitting any modulo (2k + 1)-orientations ...

This paper studies the fundamental relations among integer flows, modulo orienta- tions, integer-valued and real-valued circular flows, and monotonicity of ...