Browse issues
no. 1
Induced matching, ordered matching and Castelnuovo-Mumford regularity of bipartite graphs
Jayanthan, A. V.1; Seyed Fakhari, Seyed Amin2; Swanson, Irena3; Yassemi, Siamak4
1Department of Mathematics, I.I.T. Madras, Chennai, Tamil Nadu 600036, India
2Departamento de Matemáticas, Universidad de los Andes, Bogotá, Colombia
3Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
4Department of Mathematics, Purdue University, Indianapolis, IN 46202, USA
Algebraic Combinatorics, Volume 9 (2026) no. 1, pp. 41-50

Let $G$ be a finite simple graph and let $\operatorname{ind-match}(G)$ and $\operatorname{ord-match}(G)$ denote the induced matching number and the ordered matching number of $G$, respectively. We characterize all bipartite graphs $G$ with $\operatorname{ind-match}(G)=\operatorname{ord-match}(G)$. We establish the Castelnuovo-Mumford regularity of powers of edge ideals and depth of powers of cover ideals for such graphs.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.461
Classification: 10X99, 14A12, 11L05
Keywords: Induced matching, ordered matching, Castelnuovo-Mumford regularity, depth, edge ideal, cover ideal

Jayanthan, A. V.  1 ; Seyed Fakhari, Seyed Amin  2 ; Swanson, Irena  3 ; Yassemi, Siamak  4

1 Department of Mathematics, I.I.T. Madras, Chennai, Tamil Nadu 600036, India
2 Departamento de Matemáticas, Universidad de los Andes, Bogotá, Colombia
3 Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
4 Department of Mathematics, Purdue University, Indianapolis, IN 46202, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{ALCO_2026__9_1_41_0,
     author = {Jayanthan, A. V. and Seyed Fakhari, Seyed Amin and Swanson, Irena and Yassemi, Siamak},
     title = {Induced matching, ordered matching and {Castelnuovo-Mumford} regularity of bipartite~graphs},
     journal = {Algebraic Combinatorics},
     pages = {41--50},
     year = {2026},
     publisher = {The Combinatorics Consortium},
     volume = {9},
     number = {1},
     doi = {10.5802/alco.461},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.461/}
}
TY  - JOUR
AU  - Jayanthan, A. V.
AU  - Seyed Fakhari, Seyed Amin
AU  - Swanson, Irena
AU  - Yassemi, Siamak
TI  - Induced matching, ordered matching and Castelnuovo-Mumford regularity of bipartite graphs
JO  - Algebraic Combinatorics
PY  - 2026
SP  - 41
EP  - 50
VL  - 9
IS  - 1
PB  - The Combinatorics Consortium
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.461/
DO  - 10.5802/alco.461
LA  - en
ID  - ALCO_2026__9_1_41_0
ER  - 
%0 Journal Article
%A Jayanthan, A. V.
%A Seyed Fakhari, Seyed Amin
%A Swanson, Irena
%A Yassemi, Siamak
%T Induced matching, ordered matching and Castelnuovo-Mumford regularity of bipartite graphs
%J Algebraic Combinatorics
%D 2026
%P 41-50
%V 9
%N 1
%I The Combinatorics Consortium
%U https://alco.centre-mersenne.org/articles/10.5802/alco.461/
%R 10.5802/alco.461
%G en
%F ALCO_2026__9_1_41_0
Jayanthan, A. V.; Seyed Fakhari, Seyed Amin; Swanson, Irena; Yassemi, Siamak. Induced matching, ordered matching and Castelnuovo-Mumford regularity of bipartite graphs. Algebraic Combinatorics, Volume 9 (2026) no. 1, pp. 41-50. doi: 10.5802/alco.461

[1] Banerjee, Arindam; Beyarslan, Selvi Kara; Huy Tài, Hà Regularity of edge ideals and their powers, Advances in algebra (Springer Proc. Math. Stat.), Volume 277, Springer, Cham, 2019, pp. 17-52 | DOI | MR | Zbl

[2] Beyarslan, Selvi; Hà, Huy Tài; Trung, Trân Nam Regularity of powers of forests and cycles, J. Algebraic Combin., Volume 42 (2015) no. 4, pp. 1077-1095 | DOI | MR | Zbl

[3] Brodmann, M. The asymptotic nature of the analytic spread, Math. Proc. Cambridge Philos. Soc., Volume 86 (1979) no. 1, pp. 35-39 | DOI | MR | Zbl

[4] Cameron, Kathie; Walker, Tracy The graphs with maximum induced matching and maximum matching the same size, Discrete Math., Volume 299 (2005) no. 1-3, pp. 49-55 | DOI | MR | Zbl

[5] Constantinescu, Alexandru; Varbaro, Matteo Koszulness, Krull dimension, and other properties of graph-related algebras, J. Algebraic Combin., Volume 34 (2011) no. 3, pp. 375-400 | DOI | MR | Zbl

[6] Cutkosky, S. Dale; Herzog, Jürgen; Trung, Ngô Viêt Asymptotic behaviour of the Castelnuovo-Mumford regularity, Compositio Math., Volume 118 (1999) no. 3, pp. 243-261 | DOI | MR | Zbl

[7] Francisco, Christopher A.; Hà, Huy Tài Whiskers and sequentially Cohen-Macaulay graphs, J. Combin. Theory Ser. A, Volume 115 (2008) no. 2, pp. 304-316 | DOI | MR | Zbl

[8] Herzog, Jürgen; Hibi, Takayuki Monomial ideals, Graduate Texts in Mathematics, 260, Springer-Verlag London, Ltd., London, 2011, xvi+305 pages | DOI | MR | Zbl

[9] Hibi, Takayuki; Higashitani, Akihiro; Kimura, Kyouko; O’Keefe, Augustine B. Algebraic study on Cameron-Walker graphs, J. Algebra, Volume 422 (2015), pp. 257-269 | DOI | MR | Zbl

[10] Hibi, Takayuki; Higashitani, Akihiro; Kimura, Kyouko; Tsuchiya, Akiyoshi Dominating induced matchings of finite graphs and regularity of edge ideals, J. Algebraic Combin., Volume 43 (2016) no. 1, pp. 173-198 | DOI | MR | Zbl

[11] Hibi, Takayuki; Kimura, Kyouko; Matsuda, Kazunori; Tsuchiya, Akiyoshi Regularity and a-invariant of Cameron-Walker graphs, J. Algebra, Volume 584 (2021), pp. 215-242 | DOI | MR | Zbl

[12] Hoa, Le Tuan; Kimura, Kyouko; Terai, Naoki; Trung, Tran Nam Stability of depths of symbolic powers of Stanley-Reisner ideals, J. Algebra, Volume 473 (2017), pp. 307-323 | DOI | MR | Zbl

[13] Katzman, Mordechai Characteristic-independence of Betti numbers of graph ideals, J. Combin. Theory Ser. A, Volume 113 (2006) no. 3, pp. 435-454 | DOI | MR | Zbl

[14] Kodiyalam, Vijay Asymptotic behaviour of Castelnuovo-Mumford regularity, Proc. Amer. Math. Soc., Volume 128 (2000) no. 2, pp. 407-411 | DOI | MR | Zbl

[15] Seyed Fakhari, S. A. Depth, Stanley depth, and regularity of ideals associated to graphs, Arch. Math. (Basel), Volume 107 (2016) no. 5, pp. 461-471 | DOI | MR | Zbl

[16] Seyed Fakhari, S. A. Depth and Stanley depth of symbolic powers of cover ideals of graphs, J. Algebra, Volume 492 (2017), pp. 402-413 | DOI | MR | Zbl

[17] Seyed Fakhari, Seyed Amin; Yassemi, Siamak Improved bounds for the regularity of powers of edge ideals of graphs, J. Commut. Algebra, Volume 15 (2023) no. 1, pp. 85-98 | MR | DOI | Zbl

[18] Van Tuyl, Adam Sequentially Cohen-Macaulay bipartite graphs: vertex decomposability and regularity, Arch. Math. (Basel), Volume 93 (2009) no. 5, pp. 451-459 | DOI | MR | Zbl

[19] Van Tuyl, Adam; Villarreal, Rafael H. Shellable graphs and sequentially Cohen-Macaulay bipartite graphs, J. Combin. Theory Ser. A, Volume 115 (2008) no. 5, pp. 799-814 | DOI | MR | Zbl

[20] Villarreal, Rafael H. Cohen-Macaulay graphs, Manuscripta Math., Volume 66 (1990) no. 3, pp. 277-293 | DOI | MR | Zbl

[21] Woodroofe, Russ Matchings, coverings, and Castelnuovo-Mumford regularity, J. Commut. Algebra, Volume 6 (2014) no. 2, pp. 287-304 | DOI | MR | Zbl

Cited by Sources: