Gallai's conjecture for graphs with treewidth 3
F Botler, M Sambinelli - Electronic Notes in Discrete Mathematics, 2017 - Elsevier
Gallai conjectured (1966) that the edge-set of a simple graph G with n vertices can be
covered by at most (n+ 1)/2 edge-disjoint paths. Lovász [Lovász, L., On covering of graphs,
in: Theory of Graphs (Proc. Colloq., Tihany, 1966), Academic Press, New York, 1968 pp. 231–
236.] verified this conjecture for graphs with at most one vertex of even degree, and Pyber
[Pyber, L., Covering the edges of a connected graph by paths, J. Combin. Theory Ser. B 66
(1996), pp. 152–159.] verified it for graphs in which every cycle contains a vertex of odd …
covered by at most (n+ 1)/2 edge-disjoint paths. Lovász [Lovász, L., On covering of graphs,
in: Theory of Graphs (Proc. Colloq., Tihany, 1966), Academic Press, New York, 1968 pp. 231–
236.] verified this conjecture for graphs with at most one vertex of even degree, and Pyber
[Pyber, L., Covering the edges of a connected graph by paths, J. Combin. Theory Ser. B 66
(1996), pp. 152–159.] verified it for graphs in which every cycle contains a vertex of odd …
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