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Circuit Double Cover of Graphs by Cun-Quan Zhang

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15Beyond integer (1, 2)-weight

The faithful covering problem is introduced as a natural approach for the CDC conjecture. Although the faithful covering problem does not hold for all eulerian (1, 2)-weighted graphs ((P10, w10) is a counterexample), there are some generalizations and relaxations. Theorem 12.1.2 can be considered as a general faithful covering problem for all positive weights, while Theorem 15.1.2, Propositions 15.2.1 and 15.2.2, etc. are all considered as relaxations of the faithful covering problem.

* A uniform definition in linear/integer programming

Most of the related faithful covering problems have similar definitions in graph theory and in linear/integer programming.

Definition 15.0.1 Let G = (V, E) be a bridgeless graph ...

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