
Gallai's path decomposition conjecture for trianglefree planar graphs
A path decomposition of a graph G is a collection of edgedisjoint paths...
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Towards Gallai's path decomposition conjecture
A path decomposition of a graph G is a collection of edgedisjoint paths...
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Regular matroids have polynomial extension complexity
We prove that the extension complexity of the independence polytope of e...
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1Safe Petri nets and special cube complexes: equivalence and applications
Nielsen, Plotkin, and Winskel (1981) proved that every 1safe Petri net ...
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Fast recognition of some parametric graph families
We identify all [1, λ, 8]cycle regular Igraphs and all [1, λ, 8]cycle...
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SplitDecomposition Trees with Prime Nodes: Enumeration and Random Generation of Cactus Graphs
In this paper, we build on recent results by Chauve et al. (2014) and Ba...
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Breadthfirst search on a Ramanujan graph
The behavior of the randomized breadthfirst search algorithm is analyze...
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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 that cover the edge set of G. Favaron, Genest, and Kouider (2010) conjectured that every (2k+1)regular graph that contains a perfect matching admits a P_2k+1decomposition. They also verified this conjecture for 5regular graphs without cycles of length 4. In 2015, Botler, Mota, and Wakabayashi verified this conjecture for 5regular graphs without triangles. In this paper, we verify it for (2k+1)regular graphs that contain the kth power of a spanning cycle; and for 5regular graphs that contain special spanning 4regular Cayley graphs.
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