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For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
VBA can, however, control one application from another using OLE Automation. For example, VBA can automatically create a Microsoft Word report from Microsoft Excel data that Excel collects automatically from polled sensors. VBA can use, but not create, ActiveX/COM DLLs, and later versions add support for class modules.
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
Outerplanar graph; Random graph; Regular graph; Scale-free network; Snark (graph theory) Sparse graph. Sparse graph code; Split graph; String graph; Strongly regular graph; Threshold graph; Total graph; Tree (graph theory). Trellis (graph) Turán graph; Ultrahomogeneous graph; Vertex-transitive graph; Visibility graph. Museum guard problem ...
The "pearls" of the title include theorems, proofs, problems, and examples in graph theory.The book has ten chapters; after an introductory chapter on basic definitions, the remaining chapters material on graph coloring; Hamiltonian cycles and Euler tours; extremal graph theory; subgraph counting problems including connections to permutations, derangements, and Cayley's formula; graph ...
Graph theory is the branch of mathematics that examines the properties of mathematical graphs. See glossary of graph theory for common terms and their definition. Informally, this type of graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs), which can also have associated directions. Typically, a graph ...
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In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. [2]