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In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points ) and each of the related pairs of vertices is called an edge (also called link or line ...
The discharging method is used to prove that every graph in a certain class contains some subgraph from a specified list. The presence of the desired subgraph is then often used to prove a coloring result. [1] Most commonly, discharging is applied to planar graphs. Initially, a charge is assigned to each face and each vertex of the graph. The ...
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).
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.
A d-claw in a graph is a set of d+1 vertices, one of which (the "center") is connected to the other d vertices, but the other d vertices are not connected to each other. A d-claw-free graph is a graph that does not have a d-claw subgraph. Consider the algorithm that starts with an empty set, and incrementally adds an arbitrary vertex to it as ...
Download as PDF; Printable version; ... Theorems in graph theory (1 C, 54 P) Pages in category "Theorems in discrete mathematics"
The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics.It provides one of two known approaches to solving the graph realization problem, i.e. it gives a necessary and sufficient condition for a finite sequence of natural numbers to be the degree sequence of a simple graph.
A graph that can be proven non-Hamiltonian using Grinberg's theorem. In graph theory, Grinberg's theorem is a necessary condition for a planar graph to contain a Hamiltonian cycle, based on the lengths of its face cycles. If a graph does not meet this condition, it is not Hamiltonian.
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