Abstract
The problem of characterizing maximal non-Hamiltonian graphs may be naturally extended to characterizing graphs that are maximal with respect to nontraceability and beyond that to -path traceability. We show how -path traceability behaves with respect to disjoint union of graphs and the join with a complete graph. Our main result is a decomposition theorem that reduces the problem of characterizing maximal -path traceable graphs to characterizing those that have no universal vertex. We generalize a construction of maximal nontraceable graphs by Zelinka to -path traceable graphs.
Citation
Kashif Bari. Michael O’Sullivan. "The Hamiltonian problem and $t$-path traceable graphs." Involve 10 (5) 801 - 812, 2017. https://doi.org/10.2140/involve.2017.10.801
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