By Martin Charles Golumbic

ISBN-10: 0122892607

ISBN-13: 9780122892608

Algorithmic Graph concept and excellent Graphs, first released in 1980, has turn into the vintage creation to the sector. This new Annals version maintains to exhibit the message that intersection graph types are an important and significant software for fixing real-world difficulties. It is still a stepping stone from which the reader may well embark on one of the interesting examine trails.

The prior 20 years were an amazingly fruitful interval of study in algorithmic graph thought and dependent households of graphs. in particular very important were the idea and functions of recent intersection graph types reminiscent of generalizations of permutation graphs and period graphs. those have result in new households of excellent graphs and plenty of algorithmic effects. those are surveyed within the new Epilogue bankruptcy during this moment version.

· new version of the "Classic" e-book at the topic

· incredible creation to a wealthy examine area

· major writer within the box of algorithmic graph theory

· superbly written for the hot mathematician or laptop scientist

· complete therapy

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**Extra resources for Algorithmic Graph Theory and Perfect Graphs**

**Sample text**

Emphasizing the significance of polynomial-time reducibility, he focused attention on NP decision problems. 1. The hierarchy of complexities. The big open question is whether or not the "zone of uncertainty," NP-P, is empty. 1. Complexity of Computer Algorithms 29 mathematical logic is NP-complete (Cook's theorem), and he suggested other problems which might be NP-complete. Karp [1972] presented a large collection of NP-complete problems (about two dozen) arising from combinatorics, logic, set theory, and other areas of discrete mathematics.

Also, H can be constructed from G in 0(n + e) steps. Finally, since OL{H) = a(G) + e, a deterministic polynomial time algorithm which solves for

Thus, a(G) can be determined from χ(Η'). | Since it is well known that STABLE SET is NP-complete, we obtain the following lesser known result. 30 2. 2. STABLE SET ON TRIANGLE-FREE GRAPHS is NP-complete. A graph theoretic or other type of problem Π which is normally hard to solve in the general case may have an efficient solution if the input domain is suitably restricted. The HAMILTONIAN CIRCUIT problem, for example, is trivial if the only graphs considered are trees. However, we have seen that restricting the STABLE SET problem to triangle-free graphs is not sufficient to allow fast calculation (until someone proves that P = NP).