Rocky Mountain Journal of Mathematics

On vertex decomposable and Cohen-Macaulay regular graphs

J. Luviano and E. Reyes

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We characterize the Cohen-Macaulay property for generalized Petersen graphs and $3$-regular graphs. In particular, we prove that these graphs are vertex decomposable. Also, we characterize pure vertex decomposability for $4$-transitive graphs without $5$-holes. Finally, we study the small cycles of well-covered and Cohen-Macaulay regular graphs.

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Rocky Mountain J. Math., Volume 48, Number 8 (2018), 2625-2651.

First available in Project Euclid: 30 December 2018

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Zentralblatt MATH identifier

Primary: 05C75: Structural characterization of families of graphs 05E45: Combinatorial aspects of simplicial complexes 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10]

Pure vertex decomposability Cohen Macaulay regular graphs generalized Petersen graphs transitive graphs and well-covered


Luviano, J.; Reyes, E. On vertex decomposable and Cohen-Macaulay regular graphs. Rocky Mountain J. Math. 48 (2018), no. 8, 2625--2651. doi:10.1216/RMJ-2018-48-8-2625.

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