Sentence examples for be an arbitrary graph from inspiring English sources

Let E be an arbitrary graph and let (mathbb {K}) be a field.

The graph E has the Countable Separation Property in case there exists a countable set S ⊆ E 0 with the property that for every v ∈ E 0 there exists s ∈ S for which v ≥ s. [10, Theorem 5.7] Let E be an arbitrary graph and K any field.

We denote by L g r ( L K ( E ) ) the collection of two-sided graded ideals of L K ( E ), and by T E the collection of pairs ( H, S ) where H is a hereditary saturated subset of E, and S ⊆ B H. [97, Theorem 5.7] Let E be an arbitrary graph and K any field.

Let be an arbitrary graph.

L emma 1 Let be an arbitrary graph.

Let G be an arbitrary graph and M the SNP-fragment matrix as defined in Lemma 1.

First, we take the link scheduling problem under a more realistic network model, the request-to-send (RTS /clear-to-send (CTS) model, undeRTS /clear-to-sendication gRTS /clear-to-senditrary geometriCTSraph.

Let (G^{sigma}) be an arbitrary oriented graph on n vertices and (V' subseteq V(G)).

Lemma 2.1 Let G σ be an arbitrary oriented graph on n vertices and V ′ ⊆ V ( G ). Suppose that | V ′ | = k.

Let G σ be an arbitrary connected oriented graph.

Let (G^{sigma}) be an arbitrary connected oriented graph.