Working with Planar Graphs part2(Machine Learning)
Partitioning edges of a planar graph into linear forests and a matching(arXiv) Author : Marthe Bonamy, Jadwiga Czyżewska, Łukasz Kowalik, Michał Pilipczuk Abstract : We show that the edges of any planar graph of maximum degree at most 9 can be partitioned into 4 linear forests and a matching. Combined with known results, this implies that the edges of any planar graph G of odd maximum degree Δ≥9 can be partitioned into Δ−12 linear forests and one matching. This strengthens well-known results stating that graphs in this class have chromatic index Δ [Vizing, 1965] and linear arboricity at most ⌈(Δ+1)/2⌉ [Wu, 1999].
Working with Planar Graphs part2(Machine Learning) Partitioning edges of a planar graph into linear forests and a matching(arXiv) Author : Marthe Bonamy, Jadwiga Czyżewska, Łukasz Kowalik, Michał Pilipczuk Abstract : We show that the edges of any planar graph of maximum degree at most 9 can be partitioned into 4 linear forests and a matching. Combined with known results, this implies that the edges of any planar graph G of odd maximum degree Δ≥9 can be partitioned into Δ−12 linear forests and one matching. This strengthens well-known results stating that graphs in this class have chromatic index Δ [Vizing, 1965] and linear arboricity at most ⌈(Δ+1)/2⌉ [Wu, 1999]. machine-learning
Working Planar Graphs part2Machine Learning Partitioning edge planar graph linear forest matchingarXiv Author Marthe Bonamy Jadwiga Czyżewska Łukasz Kowalik Michał Pilipczuk Abstract show edge planar graph maximum degree 9 partitioned 4 linear forest matching Combined known result implies edge planar graph G odd maximum degree Δ≥9 partitioned Δ−12 linear forest one matching strengthens wellknown result stating graph class chromatic index Δ Vizing 1965 linear arboricity ⌈Δ12⌉ Wu 1999 machinelearning