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Hamilton cycles and closed trails in iterated line graphs

✍ Scribed by Paul A. Catlin; Iqbalunnisa T. N. Janakiraman; N. Srinivasan

Publisher: John Wiley and Sons
Year: 1990
Tongue: English
Weight: 712 KB
Volume: 14
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190140308

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Let G be an undirected connected graph that is not a path. We define h(G) (respectively, s(G)) to be the least integer m such that the iterated line graph L^m^(G) has a Hamiltonian cycle (respectively, a spanning closed trail). To obtain upper bounds on h(G) and s(G), we characterize the least integer m such that L^m^(G) has a connected subgraph H, in which each edge of H is in a 3‐cycle and V(H) contains all vertices of degree not 2 in L^m^(G). We characterize the graphs G such that h(G) — 1 (respectively, s(G)) is greater than the radius of G.

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