15 research outputs found
Hamiltonicity in connected regular graphs
In 1980, Jackson proved that every 2-connected -regular graph with at most
vertices is Hamiltonian. This result has been extended in several papers.
In this note, we determine the minimum number of vertices in a connected
-regular graph that is not Hamiltonian, and we also solve the analogous
problem for Hamiltonian paths. Further, we characterize the smallest connected
-regular graphs without a Hamiltonian cycle.Comment: 5 page
On lower bounds for the matching number of subcubic graphs
We give a complete description of the set of triples (a,b,c) of real numbers
with the following property. There exists a constant K such that a n_3 + b n_2
+ c n_1 - K is a lower bound for the matching number of every connected
subcubic graph G, where n_i denotes the number of vertices of degree i for each
i