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The Classification of Finitely Spreading Graphs
Author(s) -
Diestel Reinhard
Publication year - 1996
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-73.3.534
Subject(s) - mathematics , combinatorics , conjecture , vertex (graph theory) , graph , bounded function , finitely generated abelian group , discrete mathematics , mathematical analysis
Thomassen introduced the concept of a finitely spreading graph: an infinite graph whose edges can be oriented, each in one, both, or neither direction, so that every vertex has finite out‐degree and every ray has a forward oriented tail. He conjectured that a graph is finitely spreading if and only if it is bounded in the sense of Halin—equivalently (see [ 5 ]), if it contains none of three specified infinitely spreading graphs. We prove Thomassen's conjecture in amended form, adding a fourth minimal obstruction to the three conjectured ones.