Subgraphs smaller than the girth | Zendy

Simoncini Luca | Zendy; Taylor Herbert | Zendy

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Subgraphs smaller than the girth

Author(s) -

Simoncini Luca,

Taylor Herbert

Publication year - 1980

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.3190040111

Subject(s) - combinatorics , mathematics , girth (graph theory) , tree (set theory) , node (physics) , path (computing) , discrete mathematics , physics , computer science , computer network , quantum mechanics

For graphs A , B , let ( B A ) denote the number of subsets of nodes of A for which the induced subgraph is B . If G and H both have girth > k , and if ( T G ) = ( T H ) for every k ‐node tree T , then for every k ‐node forest F , ( F G ) = ( G H ). Say the spread of a tree is the number of nodes in a longest path. If G is regular of degree d , on n nodes, with girth > k , and if F is a forest of total spread ≤ k , then the value of ( F G ) depends only on n and d .

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