By Lawler E.L.

ISBN-10: 0003084868

ISBN-13: 9780003084863

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**Additional info for Combinatorial optimization: networks and matroids**

**Example text**

Yet we have the habit of referring to “the” dual of a graph G, and in practice there is not much harm in this. The procedure for dualizing digraphs is essentially the same as for graphs, except that we must be able to assign directions to the arcs in the geometric dual. We do this as follows. 10 Two plane graphs of the same graph and their duals e is rotated clockwise in the plane. Place an arrowhead on the end of e* which would first touch the arrowhead of e. 11. For our purposes, the most significant property of dualization is that it interchanges cycles and cocycles.

I=l,2 . . . p, I i uijxj = hi, 1 i = p + 1, p + 2, . . , I;IZ. 1) j= xi 2 0. i = 1,2 . . . 9 + 2,. . II. ch variable xj is identified with an “activity” within a business enterprise or economic system. , the purchase of a particular raw material or the production of a certain good or service. A set of variables constitutes a “program” of operation in terms of “levels” for the various activities. g.. ) And since the constraints on the choice of a program are linear. the term “linear programming” is used.

B) Complementary graph G. (c) Three cliques in (;. (d) Subgraph induced by N = (1, 2. 41. (e) Deletion of arc (1, 3). (f) Contraction of arc (I, 3). 3 Prove that every graph has an even number of nodes of odd degree. If G = (S, 7: A) is a bipartite graph, characterize the (clique structure of G and of G. The incidence matrix ofa multigraph is defined as for an ordinary graph and the adjacency matrix can be generalized :jo that uij = the number of arcs between between i and ,j. What is the relation between A and BBT?

### Combinatorial optimization: networks and matroids by Lawler E.L.

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