2022
DOI: 10.48550/arxiv.2205.09038
|View full text |Cite
Preprint
|
Sign up to set email alerts
|

The existence of $\{p,q\}$-orientations in edge-connected graphs

Abstract: In 1976 Frank and Gyárfás gave a necessary and sufficient condition for the existence of an orientation in an arbitrary graph G such that for each vertex v, the out-degree, where p and q are two integer-valued functions on V (G) with p ≤ q. In this paper, we give a sufficient edge-connectivity condition for the existence of an orientation in G suchThis result is a generalization of a theorem due to Thomassen (2012) on the existence of modulo orientations in highly edge-connected graphs.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1

Citation Types

0
4
0

Year Published

2022
2022
2022
2022

Publication Types

Select...
2

Relationship

2
0

Authors

Journals

citations
Cited by 2 publications
(4 citation statements)
references
References 9 publications
0
4
0
Order By: Relevance
“…Remark 4.4. Note that the results of this section can be developed to version for investigating treeconnected factors with given sparse lists on degrees; similar to a result in [5] for investigating orientations with given sparse lists on out-degrees. Also, Theorem 4.3 can be stated for graphs with bi(G) ≤ k − 1, but we need to insert a stronger condition on h using the same proof.…”
Section: Graphs With Bipartite Index At Least K −mentioning
confidence: 95%
See 2 more Smart Citations
“…Remark 4.4. Note that the results of this section can be developed to version for investigating treeconnected factors with given sparse lists on degrees; similar to a result in [5] for investigating orientations with given sparse lists on out-degrees. Also, Theorem 4.3 can be stated for graphs with bi(G) ≤ k − 1, but we need to insert a stronger condition on h using the same proof.…”
Section: Graphs With Bipartite Index At Least K −mentioning
confidence: 95%
“…Theorem 3.2. ( [5]) Let G be a 4k 2 -tree-connected graph and let p and q be two integer-valued functions on…”
Section: Tools: Orientationsmentioning
confidence: 99%
See 1 more Smart Citation
“…Theorem 1.2. ( [7]) Let G be a 8k 2 -edge-connected graph and let p and q be two integer-valued functions…”
Section: Introductionmentioning
confidence: 99%