Abstract
In this paper, we give a constructive proof of the fact that the treewidth of a graph is at most its divisorial gonality. The proof gives a polynomial time algorithm to construct a tree decomposition of width at most k, when an effective divisor of degree k that reaches all vertices is given. We also give a similar result for two related notions: stable divisorial gonality and stable gonality.
This research was initiated at the Sandpiles and Chip Firing Workshop, held November 25–26, 2019 at the Centre for Complex Systems Studies, Utrecht University.
J. van Dobben de Bruyn—Supported by NWO grant 613.009.127.
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Notes
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Here we deviate from the definition of position as stated in [13] in that we allow R to consist of zero X-flaps or more than one X-flap.
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Acknowledgements
We thank Gunther Cornelissen, Bart Jansen, Erik Jan van Leeuwen, Marieke van der Wegen, and Tom van der Zanden for helpful discussions.
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Bodlaender, H.L., van Dobben de Bruyn, J., Gijswijt, D., Smit, H. (2020). Constructing Tree Decompositions of Graphs with Bounded Gonality. In: Kim, D., Uma, R., Cai, Z., Lee, D. (eds) Computing and Combinatorics. COCOON 2020. Lecture Notes in Computer Science(), vol 12273. Springer, Cham. https://doi.org/10.1007/978-3-030-58150-3_31
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