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Decomposition of Complete Graphs into Arbitrary Trees
G. Sethuraman,
Published in Springer Japan
In this paper, we propose a new conjecture that the complete graph K4m+1 can be decomposed into copies of two arbitrary trees, each of size m, m≥ 1. To support this conjecture we prove that the complete graph K4cm+1 can be decomposed into copies of an arbitrary tree with m edges and copies of the graph H, where H is either a path with m edges or a star with m edges and where c is any positive integer. Further, we discuss related open problems. © 2021, The Author(s), under exclusive licence to Springer Japan KK, part of Springer Nature.
About the journal
JournalData powered by TypesetGraphs and Combinatorics
PublisherData powered by TypesetSpringer Japan