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Balanced caterpillars of maximum degree 3 and with hairs of arbitrary length are subgraphs of their optimal hypercube
Author(s) -
Monien Burkhard,
Wechsung Gerd
Publication year - 2018
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.22175
Subject(s) - combinatorics , mathematics , degree (music) , hypercube , path (computing) , tree (set theory) , discrete mathematics , computer science , physics , acoustics , programming language
A caterpillar C is a tree having a path that contains all vertices of C of degree at least 3. We show in this article that every balanced caterpillar with maximum degree 3 and 2 n vertices is a subgraph of the n ‐dimensional hypercube. This solves a long‐standing open problem and generalizes a result of Havel and Liebl (1986), who considered only such caterpillars that have a path containing all vertices of degree at least 2.