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In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree at most k: that is, some vertex in the subgraph touches k or fewer of the subgraph's edges. The degeneracy of a graph is the smallest value of k for which it is k-degenerate.
1 Examples and types of graphs. 2 Graph coloring. 3 Paths and cycles. 4 Trees. Toggle Trees subsection. ... This is a list of graph theory topics, by Wikipedia page.
Metric k-center; Minimum degree spanning tree; Minimum k-cut; Minimum k-spanning tree; Minor testing (checking whether an input graph contains an input graph as a minor); the same holds with topological minors; Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is ...
A graph is said to be k-generated if for every subgraph H of G, the minimum degree of H is at most k. Incidence chromatic number of k-degenerated graphs G is at most ∆(G) + 2k − 1. Incidence chromatic number of K 4 minor free graphs G is at most ∆(G) + 2 and it forms a tight bound. Incidence chromatic number of a planar graph G is at most ...
Alternatively, If A is an adjacency matrix for the graph, modified to have nonzero entries on its main diagonal, then the nonzero entries of A k give the adjacency matrix of the k th power of the graph, [14] from which it follows that constructing k th powers may be performed in an amount of time that is within a logarithmic factor of the time ...
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.
These changes leave five bridges existing at the same sites that were involved in Euler's problem. In terms of graph theory, two of the nodes now have degree 2, and the other two have degree 3. Therefore, an Eulerian path is now possible, but it must begin on one island and end on the other. [9]
The complete graph on n vertices is denoted by K n.Some sources claim that the letter K in this notation stands for the German word komplett, [4] but the German name for a complete graph, vollständiger Graph, does not contain the letter K, and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory.