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Orientations of graphs avoiding given lists on out-degrees

Akbari, S ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1002/jgt.22498
  3. Publisher: Wiley-Liss Inc , 2020
  4. Abstract:
  5. Let G be a graph and F: V(G) → 2N be a mapping. The graph G is said to be F- avoiding if there exists an orientation O of G such that do +(v)∉ F (v) for every v ∈ V (G), where do +(v) denotes the out-degree of v in the directed graph G with respect to O. In this paper it is shown that if G is bipartite and |F (v)| ≤ dG (v)/2 for every v ∈ V (G), then G is F-avoiding. The bound |F (v)| ≤ dG (v)/2 is best possible. For every graph G, we conjecture that if |F (v)| ≤ 1/2 dG (v)-1) for every v ∈ V (G), then G is F-avoiding. We also argue about this conjecture for the best possibility of the conditions and also show some partial solutions. © 2019 Wiley Periodicals, Inc
  6. Keywords:
  7. F-avoiding ; Orientation ; Out-degrees ; Crystal orientation ; Geometry ; Graph theory ; Out-degrees ; Directed graphs
  8. Source: Journal of Graph Theory ; Volume 93, Issue 4 , 2020 , Pages 483-502
  9. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/jgt.22498