
Towards Gallai's path decomposition conjecture
A path decomposition of a graph G is a collection of edgedisjoint paths...
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Edgedecomposing graphs into coprime forests
The BaratThomassen conjecture, recently proved in [Bensmail et al.: A p...
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Decomposition of (2k+1)regular graphs containing special spanning 2kregular Cayley graphs into paths of length 2k+1
A P_ℓdecomposition of a graph G is a set of paths with ℓ edges in G tha...
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Parametric Shortest Paths in Planar Graphs
We construct a family of planar graphs (G_n: n≥ 1), where G_n has n vert...
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Further Evidence Towards the Multiplicative 123 Conjecture
The product version of the 123 Conjecture, introduced by SkowronekKaz...
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Multitransversals for Triangles and the Tuza's Conjecture
In this paper, we study a primal and dual relationship about triangles: ...
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Examples relating to Green's conjecture in low characteristics and genera
We exhibit approximately fifty Betti diagrams of free resolutions of rin...
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Gallai's path decomposition conjecture for trianglefree planar graphs
A path decomposition of a graph G is a collection of edgedisjoint paths of G that covers the edge set of G. Gallai (1968) conjectured that every connected graph on n vertices admits a path decomposition of cardinality at most (n+1)/2. Gallai's Conjecture has been verified for many classes of graphs. In particular, Lovász (1968) verified this conjecture for graphs with at most one vertex with even degree, and Pyber (1996) verified it for graphs in which every cycle contains a vertex with odd degree. Recently, Bonamy and Perrett (2016) verified Gallai's Conjecture for graphs with maximum degree at most 5, and Botler et al. (2017) verified it for graphs with treewidth at most 3. In this paper, we verify Gallai's Conjecture for trianglefree planar graphs.
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