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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 ...
Its authors have divided Elementary Number Theory, Group Theory and Ramanujan Graphs into four chapters. The first of these provides background in graph theory, including material on the girth of graphs (the length of the shortest cycle), on graph coloring, and on the use of the probabilistic method to prove the existence of graphs for which both the girth and the number of colors needed are ...
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 ).
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 telecommunications industry has also motivated advances in discrete mathematics, particularly in graph theory and information theory. Formal verification of statements in logic has been necessary for software development of safety-critical systems , and advances in automated theorem proving have been driven by this need.
Download as PDF; Printable version; ... Theorems in graph theory (1 C, 54 P) Pages in category "Theorems in discrete mathematics"
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 ...
The 99-graph problem asks for a 99-vertex graph with the same property. In graph theory , Conway's 99-graph problem is an unsolved problem asking whether there exists an undirected graph with 99 vertices , in which each two adjacent vertices have exactly one common neighbor, and in which each two non-adjacent vertices have exactly two common ...
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