Showing papers on "Quartic graph published in 1974"
TL;DR: In this article, a simple proof of the conjecture that the square of every two-connected graph is Hamiltonian is given, which is based on the DT-block conjecture. But this result is not applicable to DT-graphs.
188 citations
TL;DR: In this paper, it was shown that all quartic graphs can be constructed successively from a K 5 by applying two types of operations called H -type and V -type expansions.
9 citations
TL;DR: In this paper, it was shown that if G is an n-hamiltonian graph of order p > or = 5, then G sup m is (n+2m-2)-Hamiltonian for all m = 1 and n + 2m or = 3.
Abstract: : Several results on the powers of connected graphs are extended. In particular, it is shown that if G is an n-hamiltonian graph of order p > or = 5, then G sup m is (n+2m-2)-hamiltonian for all m > or = 1 and n + 2m or = 3, the graph G sup m is (P - the set((p-n)/m))-hamiltonian connected. (Author)
3 citations
01 Jan 1974
TL;DR: In this paper, conditions on the valency (minimum local degree) and the number of edges which ensure a (t, u) cover or a Hamiltonian circuit exists were given.
Abstract: Let G be a graph whose edges (x, y) have x E X, y E Y, IXI =I YI < oo. A (t, u) cover of G is a set of t edges which cover 2u vertices in both X and Y. We give conditions on the valency (minimum local degree) and the number of edges which ensure a (t, u) cover or that a Hamiltonian circuit exists.
3 citations