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- Title
Weight Choosability of Graphs with Maximum Degree 4.
- Authors
Lu, You; Li, Chong; Miao, Zheng Ke
- Abstract
Let k be a positive integer. A graph G is k-weight choosable if, for any assignment L(e) of k real numbers to each e ∈ E(G), there is a mapping f: E(G) → ℝ such that f (uv) ∈ L(uv) and ∑ e ∈ ∂ (u) f (e) ≠ ∑ e ∈ ∂ (v) f (e) for each uu ∈ E(G), where ∂(v) is the set of edges incident with v. As a strengthening of the famous 1-2-3-conjecture, Bartnicki, Grytczuk and Niwcyk [Weight choosability of graphs. J. Graph Theory, 60, 242–256 (2009)] conjecture that every graph without isolated edge is 3-weight choosable. This conjecture is wildly open and it is even unknown whether there is a constant k such that every graph without isolated edge is k-weight choosable. In this paper, we show that every connected graph of maximum degree 4 is 4-weight choosable.
- Subjects
GRAPH connectivity; REAL numbers; GEOMETRIC vertices; ASSIGNMENT problems (Programming); GRAPH labelings
- Publication
Acta Mathematica Sinica, 2020, Vol 36, Issue 6, p723
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-020-9371-8