Notes in lecture2 - trees

To Subscribe, use this Key

Status	Last Update	Fields
Published	09/30/2023	connected graph
Published	09/30/2023	component of a graph
Published	09/30/2023	Let G be a graph such that {{c1::\(δ(G) \geq 2\)}}. Then G contains* {{c2::a path of length at least \(δ(G)\)}}* {{c2::a cycle of length at least…
Published	09/30/2023	bridge
Published	09/30/2023	Let \(e∈E(G)\). Then{{c1::e is a bridge}} \(⇔\) {{c2::e is not contained in a cycle}}
Published	09/30/2023	forest
Published	09/30/2023	tree
Published	09/30/2023	leaf of a tree
Published	09/30/2023	Do all trees have leaves?
Published	09/30/2023	Let \(W ⊂ V(G)\). What do we mean by \(G \setminus W\)?
Published	09/30/2023	characterisation of tree by removing a vertex
Published	09/30/2023	spanning tree
Published	09/30/2023	Sufficient condition for spanning tree
Published	09/30/2023	{{c1::G is a tree}}⇔ {{c2::Any pair of vertices in G is linked by a unique path}}⇔ {{c3::G is connected and \(\|E\| = \|V\|-1\)}}⇔ {{c4…
Published	09/30/2023	characterisation of forest using amount of components t
Published	09/30/2023	spanning forest
Published	09/30/2023	Algorithm for finding the spanning forest of a graph \(G=(V,E)\)
Published	09/30/2023	For a graph (G=(V,E)\) with \(E= \{e_1, ..., e_q\}\) {{c2::an arbitrary ordering of the edges.}}Inductively construct\[E_0 := {{c2::∅}}\]\[ E_i =…
Published	09/30/2023	How can you tell a forest apart from a tree?
Status	Last Update	Fields