Cohen-Macaulay type of the face poset of a plane graph
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説明
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 $$\left[ {\sum\limits_\upsilon {2\left\{ {\delta _G (v) + v_G (v) - 1} \right\}} } \right] + 1$$ .
収録刊行物
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- Graphs and Combinatorics
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Graphs and Combinatorics 10 133-138, 1994-06-01
Springer Science and Business Media LLC
