Bari, Kashif; O’Sullivan, Michael E. The Hamiltonian problem and \(t\)-path traceable graphs. (English) Zbl 1364.05042 Involve 10, No. 5, 801-812 (2017). Summary: 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 \(t\)-path traceability. We show how \(t\)-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 \(t\)-path traceable graphs to characterizing those that have no universal vertex. We generalize a construction of maximal nontraceable graphs by Zelinka to \(t\)-path traceable graphs. Cited in 1 Document MSC: 05C45 Eulerian and Hamiltonian graphs Keywords:maximal non-Hamiltonian; Hamiltonian; graph theory; \(t\)-path traceable PDFBibTeX XMLCite \textit{K. Bari} and \textit{M. E. O'Sullivan}, Involve 10, No. 5, 801--812 (2017; Zbl 1364.05042) Full Text: DOI arXiv References: [1] ; Bullock, Electron. J. Combin., 15 (2008) [2] 10.1016/0012-365X(73)90138-6 · Zbl 0256.05122 · doi:10.1016/0012-365X(73)90138-6 [3] 10.1016/0012-365X(82)90145-5 · Zbl 0481.05038 · doi:10.1016/0012-365X(82)90145-5 [4] 10.1016/0012-365X(91)90314-R · Zbl 0757.05064 · doi:10.1016/0012-365X(91)90314-R [5] 10.2140/pjm.1975.58.159 · Zbl 0264.05122 · doi:10.2140/pjm.1975.58.159 [6] 10.1007/BF02412090 · Zbl 0103.39702 · doi:10.1007/BF02412090 [7] ; Skupień, Rostock. Math. Kolloq., 97 (1979) [8] 10.7151/dmgt.1076 · Zbl 0935.05062 · doi:10.7151/dmgt.1076 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.