contemporaneously with and independently of Erdős and Rényi. In the model of Erdős and Rényi, all graphs on a fixed vertex set with a fixed number of edges...

Erdős on Graphs: His Legacy of Unsolved Problems is a book on unsolved problems in mathematics collected by Paul Erdős in the area of graph theory. It...

found four graphs on 24 vertices in which the only power-of-two cycles have 16 vertices. One of these four graphs is planar; however, the Erdős–Gyárfás conjecture...

then the union of the graphs can be properly colored with k colors. More unsolved problems in mathematics In graph theory, the Erdős–Faber–Lovász conjecture...

Paul Erdős (Hungarian: Erdős Pál [ˈɛrdøːʃ ˈpaːl]; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians...

areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős–Rényi model for graphs with general degree...

mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects, and in many cases Erdős offered...

The Erdős number (Hungarian: [ˈɛrdøːʃ]) describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship...

for the whole graph. The theorem was proved by Nicolaas Govert de Bruijn and Paul Erdős (1951), after whom it is named. The De Bruijn–Erdős theorem has...

In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability...

congruent numbers. Erdős–Moser problem: is 1 1 + 2 1 = 3 1 {\displaystyle 1^{1}+2^{1}=3^{1}} the only solution to the Erdős–Moser equation? Erdős–Straus conjecture:...

extremal graph theory, the Erdős–Stone theorem is an asymptotic result generalising Turán's theorem to bound the number of edges in an H-free graph for a...

complete graphs in the Diophantine plane for which the length of all edges are integers (unit distance graphs). Thus, Erdős–Diophantine graphs are exactly...

equivalent to the Erdős–Gallai theorem. Similar theorems describe the degree sequences of simple directed graphs, simple directed graphs with loops, and...

well-studied collaboration graphs include: Collaboration graph of mathematicians also known as the Erdős collaboration graph, where two mathematicians...

the Erdős–Ko–Rado theorem limits the number of sets in a family of sets for which every two sets have at least one element in common. Paul Erdős, Chao...

assumption of the axiom of choice. This is the de Bruijn–Erdős theorem of de Bruijn & Erdős (1951). If a graph admits a full n-coloring for every n ≥ n0, it admits...

associated to the graph, such as the Colin de Verdière number. Two graphs are called cospectral or isospectral if the adjacency matrices of the graphs are isospectral...

Erdős–Diophantine graph, an inextensible system of integer points with integer distances. The Erdős–Anning theorem inspired the Erdős–Ulam problem on...

Paul Erdős: de Bruijn–Erdős theorem (graph theory) de Bruijn–Erdős theorem (incidence geometry) Davenport–Erdős theorem Erdős–Anning theorem Erdős–Beck...

concept of the Erdős number, a measure of distance from Erdős in the collaboration network of mathematicians; his many works with Erdős include two books...

most 3n maximal cliques. The graphs meeting this bound are the Moon–Moser graphs K3,3,..., a special case of the Turán graphs arising as the extremal cases...

a joint publication with Erdős on extremal problems in graph theory, written when he was in high school in 1962. With Erdős's recommendation to Harold...

cases, non-isomorphic graphs have the same degree sequence. The degree sequence problem is the problem of finding some or all graphs with the degree sequence...

S2CID 9238219. Erdős, Paul (1947), "Some remarks on the theory of graphs", Bull. Amer. Math. Soc., 53 (4): 292–294, doi:10.1090/S0002-9904-1947-08785-1. Erdős, P...

problems in mathematics In graph theory, a branch of mathematics, the Erdős–Hajnal conjecture states that families of graphs defined by forbidden induced...

The De Bruijn–Erdős theorem may refer to: De Bruijn–Erdős theorem (incidence geometry) De Bruijn–Erdős theorem (graph theory) This disambiguation page...

10: 116–117 Erdős, Paul (1967), "Problem 2", In Theory of Graphs, Proc. Colloq., Tihany, p. 361 Jensen, T. R.; Toft, B. (1995), Graph coloring problems...

equivalently defined as graphs with clique number ≤ 2, graphs with girth ≥ 4, graphs with no induced 3-cycle, or locally independent graphs. By Turán's theorem...

graph shown, with all vertex degrees equal to four, has no Eulerian line. The infinite graphs that contain Eulerian lines were characterized by Erdős...