CoEulerian graphs

Sandpile groups and the coeulerian property for random directed graphs

We consider random directed graphs, and calculate the distribution of the cokernels of their laplacian, following the methods used by Wood. As a corollary, we show that the probability that a random digraph is coeulerian is asymptotically upper bounded by a constant around $0.43$.

Chip-firing based methods in the Riemann--Roch theory of directed graphs

Baker and Norine proved a Riemann--Roch theorem for divisors on undirected graphs. The notions of graph divisor theory are in duality with the notions of the chip-firing game of Björner, Lovász and Shor. We use this connection to prove Riemann--Roch-type results on directed graphs. We give a simple proof for a Riemann--Roch inequality on Eulerian directed graphs, improving a result of Amini and Manjunath. We also study possibilities and impossibilities of Riemann--Roch-type equalities in strongly connected digraphs and give examples. We intend to make the connections of this theory to graph th…

Chip-firing 博弈的有限记录集

Finite record sets of chip-firing games

本文研究 chip-firing 博弈的记录集，在记录集有限且仅发射两个顶点的假设下，发现了两个新性质以刻画图的记录集。

Flow-Firing 的三区域定理

A Three-Regime Theorem for Flow-Firing

本文研究 2 维胞腔复形上的流重路由点火系统，借鉴前人工作，回答了该过程是否终止及终止是否唯一的问题，提出了完全判定系统终止性的三区域定理。