Cohen-Macaulay type of the face poset of a plane graph

DOI

Search this article

Description

How can we calculate the Cohen-Macaulay type of a Cohen-Macaulay poset? This paper is an extension of earlier results in [2]. We give an explicit formula for the Cohen-Macaulay type of the face poset of a plane graph. Let G be a finite connected plane graph allowing loops and multiple edges and G* the subgraph obtained by removing all loops from G. For each vertexv of G the number of connected components of G* --v is denoted by ?G (v). Also, writev G (v) for the number of loops of G incident tov. Then the Cohen-Macaulay type of the face poset of G is $$\left[ {\sum\limits_\upsilon {2\left\{ {\delta _G (v) + v_G (v) - 1} \right\}} } \right] + 1$$ .

Journal

Details 詳細情報について

  • CRID
    1870583643047110144
  • DOI
    10.1007/bf02986657
  • ISSN
    14355914
    09110119
  • Data Source
    • OpenAIRE

Report a problem

Back to top