A new view toward vertex decomposable graphs

DOI10.1016/j.disc.2022.112953zbMath1491.05205OpenAlexW4229012412MaRDI QIDQ2144504

Jin Guo, Meiyan Li, Tong Suo Wu

Publication date: 14 June 2022

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2022.112953

zbMATH Keywords

Cohen-Macaulayvertex decomposableclosed neighbourhoodstrongly shellable

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Combinatorial aspects of commutative algebra (05E40) General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) (13A70)

Cites Work

• Unnamed Item
• Algebraic study on Cameron-Walker graphs
• Obstructions to shellability, partitionability, and sequential Cohen-Macaulayness
• Graphs with many copies of a given subgraph
• Blow-up lemma
• The graphs with maximum induced matching and maximum matching the same size
• Expansion of a simplicial complex
• Cohen–Macaulay Graphs and Face Vectors of Flag Complexes
• ON THE STRUCTURE OF COMAXIMAL GRAPHS OF COMMUTATIVE RINGS WITH IDENTITY
• Vertex decomposable graphs and obstructions to shellability
• Sequentially Cohen-Macaulay edge ideals
• Shellable Cactus Graphs
• Monomial Ideals
• Boolean graphs are Cohen–Macaulay

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