Given n points in the Euclidean plane, the degree-δ minimum spanning tree (MST) problem asks for a spanning tree of minimum weight in which the degree of each vertex is at most δ. The problem is NP-hard for 2 ≤ δ ≤ 3, while the NP-hardness of the problem is open for δ = 4. The problem is polynomial-time solvable when δ = 5. By presenting an improved approximation analysis for Chan's degree-4 MST algorithm [T. Chan, Euclidean bounded-degree spanning tree ratios, Discrete & Computational Geometry 32 (2004) 177-194], we show that, for any arbitrary collection of points in the Euclidean plane, there always exists a degree-4 spanning tree of weight at most (sqrt(2) + 2) / 3 < 1.1381 times the weight of an MST.
Jothi, R., & Raghavachari, B. (2009). Degree-bounded minimum spanning trees. Discrete Applied Mathematics, 157(5), 960–970. https://doi.org/10.1016/j.dam.2008.03.037