Subdivision Graph Research Articles

Subdivisions of graphs with large minimum degree

AbstractWe prove a theorem on path systems implying the conjecture of Bollobás that there exists a function f(k, m) (where k and m are natural numbers) satisfying the following: For each graph G of minimum degree at least f(k, m) there exists a graph H of minimum degree at least k such that G contains the graph obtained from H by subdividing each edge m times.

Forbidden subgraphs and hamiitonian properties in the square of a connected graph

AbstractVarious Harniltonian‐like properties are investigated in the squares of connected graphs free of some set of forbidden subgraphs. The star K1,4 the subdivision graph of K1,3, and the subdivision graph of K1,3 minus an endvertex play central roles. In particular, we show that connected graphs free of the subdivision graph of K1,3 minus an endvertex have vertex pancyclic squares.

On the characteristic polynomial of the adjacency matrix of the subdivision graph of a graph

The characteristic polynomial of the adjacency matrix of the subdivision graph G is related to the characteristic polynomials of the adjacency matrices of g and its line graph.