# Chip-firing games on Eulerian digraphs and -hardness of computing the rank of a divisor on a graph

@article{Kiss2015ChipfiringGO, title={Chip-firing games on Eulerian digraphs and -hardness of computing the rank of a divisor on a graph}, author={Viktor Kiss and Lilla T{\'o}thm{\'e}r{\'e}sz}, journal={Discret. Appl. Math.}, year={2015}, volume={193}, pages={48-56} }

## 16 Citations

### On approximating the rank of graph divisors

- Mathematics, Computer ScienceArXiv
- 2022

This paper strengthens Kiss and T´othm´eresz's result by establishing a connection between chip-ﬁring games and the Minimum Target Set Selection problem, and shows that the rank is diﬃcult to approximate to within a factor of O (2 log 1 − ε n ) for any ε > 0 unless P = NP.

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

- MathematicsEur. J. Comb.
- 2019

### On Computation of Baker and Norine's Rank on Complete Graphs

- MathematicsElectron. J. Comb.
- 2016

An algorithm for the determination of the rank of configurations for the complete graph K_n and an apparently new parameter which is called the prerank is presented which provides an alternative description to some well known $ q,t$-Catalan numbers.

### CoEulerian graphs

- Mathematics
- 2015

We suggest a measure of “Eulerianness” of a finite directed graph and define a class of “coEulerian” graphs. These are the graphs whose Laplacian lattice is as large as possible. As an application,…

### Sparse Graphs of High Gonality

- MathematicsSIAM J. Discret. Math.
- 2018

It is shown that there are connected graphs of treewidth 2 of arbitrarily high gonality and that there exist pairs of connected graphs such that H has strictly lower gonality than G.

### Computing divisorial gonality is hard

- Mathematics
- 2015

The gonality gon(G) of a graph G is the smallest degree of a divisor of positive rank in the sense of Baker-Norine. In this note we show that computing gon(G) is NP-hard by a reduction from the…

### Linear time algorithm for computing the rank of divisors on cactus graphs

- Computer Science, MathematicsArXiv
- 2016

A linear time algorithm is described for computing rank of divisor on graph limited on cactus graphs and it is shown that this problem is NP-hard.

### graph gonality is hard.

- Mathematics
- 2022

The divisorial gonality of a graph G, denoted by dgon(G) is the smallest degree of a divisor of positive rank in the sense ofM. Baker and S. Norine [Adv. Math. 215, No. 2, 766–788 (2007; Zbl…

## References

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The paper by M. Baker and S. Norine in 2007 introduced a new parameter on configurations of graphs and gave a new result in the theory of graphs which has an algebraic geometry flavour. This result…

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### NP-hardness of minimum feedback arc set problem on Eulerian digraphs and minimum recurrent configuration problem of Chip-firing game

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This paper points out a close relationship between MINREC and the minimum feedback arc set (MINFAS) problem on Eulerian directed graphs, and proves that both problems are NP-hard.

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### Feedback Arc Set Problem and NP-Hardness of Minimum Recurrent Configuration Problem of Chip-Firing Game on Directed Graphs

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This paper points out a close relationship between MINREC and the minimum feedback arc set (MINFAS) problem on Eulerian directed graphs, and proves that both problems are NP-hard.