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Pages in category "Unsolved problems in graph theory". The following 32 pages are in this category, out of 32 total. This list may not reflect recent changes .
A drawing of a graph. In mathematics, 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 ).
A graph with six vertices and seven edges. 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 ...
In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex can reach a vertex (and is reachable from ) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with and ends with . In an undirected graph, reachability between all pairs of vertices can be determined by ...
Component (graph theory) In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting of the ...
A 9-vertex graph in which every edge belongs to a unique triangle and every non-edge is the diagonal of a unique quadrilateral. 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 ...
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