Michael Ferrara

Pan- H -Linked Graphs

Let H be a multigraph, possibly containing loops. An H-subdivision is any simple graph obtained by replacing the edges of H with paths of arbitrary length. Let H be an arbitrary multigraph of order k, size m, n0(H) isolated vertices and n1(H) vertices of degree one. In Gould and Whalen (Graphs Comb. 23:165–182, 2007) it was shown that if G is a simple graph of order n containing an H-subdivision

tKp -saturated graphs of minimum size

{\mathcal{H}}

Cycle Lengths in Hamiltonian Graphs with a Pair of Vertices Having Large Degree Sum

and

Characterizing degree-sum maximal nonhamiltonian bipartite graphs

{\delta(G) \ge \frac{n+m-k+n_1(H)+2n_0(H)}{2}}

H

, then G contains a spanning H-subdivision with the same ground set as