PRISM Collection:http://hdl.handle.net/1880/453282017-04-29T14:07:06Z2017-04-29T14:07:06ZHALIN GRAPHS AND THE TRAVELLING SALESMAN PROBLEMCornuejols, G.Naddef, D.Pulleyblank, W.R.http://hdl.handle.net/1880/456102008-02-26T22:41:23Z1981-11-01T00:00:00ZTitle: HALIN GRAPHS AND THE TRAVELLING SALESMAN PROBLEM
Authors: Cornuejols, G.; Naddef, D.; Pulleyblank, W.R.
Abstract: A Halin graph $H = T cup C$ is obtained by imbedding a tree
$T$ having no degree two nodes in the plane, and then adding a cycle
$C$ to join the leaves of $T$ in such a way that the resulting
graph is planar. These graphs are edge minimal 3-connected, hamiltonian,
and in general have large numbers of hamilton cycles. We show that for
arbitrary real edge costs the travelling salesman problem can be
polynomially solved for such a graph, and we give an explicit
linear description of the travelling salesman polytope (the convex
hull of the incidence vectors of the hamilton cycles) for such
a graph.1981-11-01T00:00:00ZA LINEAR PROGRAMMING RELAXATION OF THE NODE PACKING PROBLEM OR
2-BICRITICALGRAPHS AND NODE COVERSPulleyblank, William R.http://hdl.handle.net/1880/456092008-02-26T22:41:18Z1978-03-01T00:00:00ZTitle: A LINEAR PROGRAMMING RELAXATION OF THE NODE PACKING PROBLEM OR
2-BICRITICALGRAPHS AND NODE COVERS
Authors: Pulleyblank, William R.
Abstract: The problem of finding a minimum cardinality set of nodes
in a graph which meet every edge is of considerable theoretical as well as
practical interest. Because of the difficulty of this problem, a linear
relaxation of an integer programming model is sometimes used as a
heuristic. In fact Nemhauser and Trotter showed that any variables
which receive integer values in an optimal solution to the relaxation
can retain the same values in an optimal solution to the integer
program.
We define 2-bicritical graphs and give several characterizations of
them.
One characterization is that they are precisely the graphs for which
an optimal solution to the linear relaxation will have no integer
valued variables. Then we show that almost all graphs are 2-bicritical,
and hence the linear relaxation almost never helps.1978-03-01T00:00:00ZMIXED DOUBLES TABLE TENNIS TOURNAMENTSPulleyblank, W.R.http://hdl.handle.net/1880/456082008-02-26T22:41:12Z1976-01-01T00:00:00ZTitle: MIXED DOUBLES TABLE TENNIS TOURNAMENTS
Authors: Pulleyblank, W.R.
Abstract: No Abstract1976-01-01T00:00:00Z