The number of spanning trees in 4-regular simple graphs

HIGHLIGHTS

• What: Extending an earlier work by Kostochka for subcubic graphs the authors show that a connected graph G with minimum degree 2 and maximum degree 4 has at least 75n4 /5+n3 /10+1/5 spanning trees where ni is the number of vertices of degree i in G unless G is the complete graph on 5 vertices or obtained from the complete graph on 6 vertices by deleting the edges of a perfect matching. In this work, Kostochka also addressed one of Alon`s question: can the authors determine exact values of c(d)? The aim . . .
  

   

  

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