Paper Info
Title
Cohen-Macaulay type of the face poset of a plane graph
Abstract
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 $$\\left[ {\\sum\\limits_\\upsilon {2\\left\\{ {\\delta _G (v) + v_G (v) - 1} \\right\\}} } \\right] + 1$$ .
Year
DOI
Venue
1994
10.1007/BF02986657
Graphs and Combinatorics
Keywords
Field
DocType
plane graph,connected component
Topology,Discrete mathematics,Combinatorics,Polynomial ring,Connected component,Multiple edges,Mathematics,Partially ordered set,Planar graph
Journal
Volume
Issue
ISSN
10
2-4
1435-5914
Citations 
PageRank 
References 
0
0.34
1
Authors
1
Name
Order
Citations
PageRank
Takayuki Hibi19430.08