The covered components polynomial: A new representation of the edge elimination polynomial

Details The covered components polynomial: A new representation of the edge elimination polynomial The covered components polynomial: A new representation of the edge elimination polynomial

2011-03-11

arxiv.org/abs/1103.2218v2

The Electronic Journal of Combinatorics 19 (2012), #50

Mathematics

Combinatorics

30 pages, 3 figures

Scientific paper

Motivated by the definition of the edge elimination polynomial of a graph we define the covered components polynomial counting spanning subgraphs with respect to their number of components, edges and covered components. We prove a recurrence relation, which shows that both graph polynomials are substitution instances of each other. We give some properties of the covered components polynomial and some results concerning relations to other graph polynomials.

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