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The Hamiltonian problem and \(t\)-path traceable graphs. (English) Zbl 1364.05042

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.

MSC:

05C45 Eulerian and Hamiltonian graphs
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[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
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