Abstract
Let \(L_n\) be a line graph with n edges and \({{\mathcal {F}}}(L_n)\) be the facet ideal of its matching complex. In this paper, we provide the irreducible decomposition of \({{\mathcal {F}}}(L_n)\) and some exact formulas for the projective dimension and regularity of \({{\mathcal {F}}}(L_n)\).
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Acknowledgements
The authors are grateful to the computer algebra systems CoCoA [3] for providing us with a large number of examples. This research is supported by the National Natural Science Foundation of China (No. 11271275), by the Natural Science Foundation of Jiangsu Province and by foundation of the Priority Academic Program Development of Jiangsu Higher Education Institutions. Finally, the authors would like to thank the referees who read carefully the manuscript and gave very helpful comments, which improved the paper both in mathematics and presentation.
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Zhu, G., Wang, H. & Cui, Y. The facet ideals of matching complexes of line graphs. J Algebr Comb 56, 955–967 (2022). https://doi.org/10.1007/s10801-022-01139-w
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DOI: https://doi.org/10.1007/s10801-022-01139-w