𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Counting patterns in graphs

✍ Scribed by Guido Guardabassi


Book ID
107883985
Publisher
Elsevier Science
Year
1972
Tongue
English
Weight
326 KB
Volume
13
Category
Article
ISSN
0095-8956

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A general formula is derivedfor the matching polynomial of an arbitrary graph G. This yields a methodfor counting matchings in graphs. From the general formula, explicit formulae are deducedfor the number of k-matchings in several well-known families of graphs.

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Let Forb",, (H) denote the class of all H-free graphs on n (labelled) vertices with m edges. In this note we estimate the cardinality of IForb,, by establishing good bounds for the probability that a random graph in the G(n,m)-model does not contain a given subgraph.