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In computer science and graph theory, the maximum weight matching problem is the problem of finding, in a weighted graph, a matching in which the sum of weights is maximized. A special case of it is the assignment problem , in which the input is restricted to be a bipartite graph , and the matching constrained to be have cardinality that of the ...
In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is planar if and only if its crossing number is zero. Determining the crossing number continues to be of great importance in graph drawing, as user studies have shown that drawing graphs with ...
A minor of an undirected graph G is any graph that may be obtained from G by a sequence of zero or more contractions of edges of G and deletions of edges and vertices of G.The minor relationship forms a partial order on the set of all distinct finite undirected graphs, as it obeys the three axioms of partial orders: it is reflexive (every graph is a minor of itself), transitive (a minor of a ...
Fixed point logics, and extensions of these logics that also allow integer counting variables whose values range from 0 to the number of vertices, have been used in descriptive complexity in an attempt to provide a logical description of decision problems in graph theory that can be decided in polynomial time. The fixed point of a logical ...
In graph theory, a branch of mathematics, graph canonization is the problem of finding a canonical form of a given graph G.A canonical form is a labeled graph Canon(G) that is isomorphic to G, such that every graph that is isomorphic to G has the same canonical form as G.
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Unsolved problems in graph theory" The following 32 pages are in this ...
Decomposition of the complete graph into three copies of +, solving the Oberwolfach problem for the input (,). In mathematics, the Oberwolfach problem is an open problem that may be formulated either as a problem of scheduling seating assignments for diners, or more abstractly as a problem in graph theory, on the edge cycle covers of complete graphs.
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.