- Tytuł:
- Triangle Decompositions of Planar Graphs
- Autorzy:
-
Mynhardt, Christina M.
Bommel, Christopher M. van - Powiązania:
- https://bibliotekanauki.pl/articles/31340823.pdf
- Data publikacji:
- 2016-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
planar graphs
triangle decompositions
rational triangle decompositions - Opis:
- A multigraph G is triangle decomposable if its edge set can be partitioned into subsets, each of which induces a triangle of G, and rationally triangle decomposable if its triangles can be assigned rational weights such that for each edge e of G, the sum of the weights of the triangles that contain e equals 1. We present a necessary and sufficient condition for a planar multigraph to be triangle decomposable. We also show that if a simple planar graph is rationally triangle decomposable, then it has such a decomposition using only weights 0, 1 and 1/2 . This result provides a characterization of rationally triangle decomposable simple planar graphs. Finally, if G is a multigraph with K4 as underlying graph, we give necessary and sufficient conditions on the multiplicities of its edges for G to be triangle and rationally triangle decomposable.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 643-659
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł