O'Reilly logo

Circuit Double Cover of Graphs by Cun-Quan Zhang

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

3Circuit chain and Petersen minor

3.1 Weight decomposition and removable circuit

Definition 3.1.1 Let (G, w) be an eulerian weighted graph. A set of eulerian weighted subgraphs {(Gi, wi) : i = 1, …, t} is called an eulerian weight decomposition of (G, w) if each Gi is a subgraph of G and images for every eE(G) (where wi(e) = 0 if eE(Gi)). (See Figure 3.1 where t = 2.)

Definition 3.1.2 Let (G, w) be an admissible eulerian weighted graph. An eulerian weight decomposition {(Gi, wi) : i = 1, …, t} of (G, w) is admissible if each (Gi, wi) is admissible. (See Figure 3.1.)

Definition 3.1.3 Let (G, w) be an admissible eulerian weighted graph. If (G, w ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required