Algebraic shifting of finite graphs

Research output: Contribution to journalArticle

Abstract

In the present article, for bipartite graphs and chordal graphs, their exterior algebraic shifted graph and their symmetric algebraic shifted graph are studied. First, we will determine the symmetric algebraic shifted graph of complete bipartite graphs. It turns out that for a ≥ 3 and b ≥ 3, the exterior algebraic shifted graph of the complete bipartite graph Ka,b of size a, b is different from the symmetric algebraic shifted graph of Ka,b. Second, we will show that the exterior algebraic shifted graph of any chordal graph G coincides with the symmetric algebraic shifted graph of G. In addition, it will be shown that the exterior algebraic shifted graph of any chordal graph G is equal to some combinatorial shifted graph of G.

Original languageEnglish
Pages (from-to)3071-3094
Number of pages24
JournalCommunications in Algebra
Volume35
Issue number10
DOIs
Publication statusPublished - 2007 Oct 1
Externally publishedYes

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Finite Graph
Graph in graph theory
Chordal Graphs
Complete Bipartite Graph
Bipartite Graph

Keywords

  • Algebraic shifting
  • Bipartite graphs
  • Chordal graphs
  • Generic initial ideals

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Algebraic shifting of finite graphs. / Murai, Satoshi.

In: Communications in Algebra, Vol. 35, No. 10, 01.10.2007, p. 3071-3094.

Research output: Contribution to journalArticle

Murai, Satoshi. / Algebraic shifting of finite graphs. In: Communications in Algebra. 2007 ; Vol. 35, No. 10. pp. 3071-3094.
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