Full Degree Spanning Trees in Random Regular Graphs
نویسندگان
چکیده
منابع مشابه
Spanning Trees in Regular Graphs
Let X be a regular graph with degree k 2 3 and order n. Then the number of spanning trees of X is where yk, ck and (3,,k(l/k) are positive constants, and p, is the number of equivalence classes of certain closed walks of length i in X. The value (k-l)k-l Ck = (k2_2k)"i/2)-l is shown to be the best possible in the sense that K(x~)"" +c^ for some increasing sequence X,, X2,.. . of regular graphs ...
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Consider a connected r-regular n-vertex graph G with random independent edge lengths, each uniformly distributed on (0,1). Let mst(G) be the expected length of a minimum spanning tree. We show that mst(G) can be estimated quite accurately under two distinct circumstances. Firstly, if r is large and G has a modest edge expansion property then mst(G) ∼ r ζ(3), where ζ(3) = ∑∞ j=1 j −3 ∼ 1.202. Se...
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ژورنال
عنوان ژورنال: Social Science Research Network
سال: 2023
ISSN: ['1556-5068']
DOI: https://doi.org/10.2139/ssrn.4334371