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Words: 3k
Articles: 123
Table of contents
3k
123
Binomial random graph
Graph theory
144
3
Clique count in a binomial random graph
Binomial random graph
24
Triangle count in a binomial random graph
Binomial random graph
29
Triangle with an attached leaf in a binomial random graph
Binomial random graph
68
Graph
Graph theory
60
4
Vertex of a graph
Graph
13
Isomorphic graphs
Graph
12
Triangle in a graph
Graph
27
1
Triangle-free graph
Triangle in a graph
7
Graph colouring
Graph theory
186
6
Chromatic number
Graph colouring
41
1
Brooks' theorem
Chromatic number
23
Edge chromatic number
Graph colouring
21
Chromatic polynomial
Graph colouring
101
2
Deletion-contraction recurrence for the chromatic polynomial
Chromatic polynomial
47
Chromatic polynomial after attaching a leaf
Chromatic polynomial
27
Independent set
Graph theory
25
Leaf of a graph
Graph theory
8
Edge of a graph
Graph theory
20
Path in a graph
Graph theory
51
2
Long path from minimum degree
Path in a graph
18
Erdos-Gallai path edge bound
Path in a graph
15
Subgraph
Graph theory
85
2
Induced subgraph
Subgraph
22
Three-colourable two-thirds subgraph lemma
Subgraph
42
Complete graph
Graph theory
58
2
Clique
Complete graph
24
Adjacency-matrix quadratic relation for a complete graph
Complete graph
20
Graph Laplacian
Graph theory
49
1
Laplacian spectrum of a complete graph
Graph Laplacian
24
Minimum-cost flow
Graph theory
40
Extremal graph theory
Graph theory
160
6
Extremal number
Extremal graph theory
34
1
Mantel theorem
Extremal number
12
Turan theorem
Extremal graph theory
126
3
Quadratic Turan edge bound
Turan theorem
9
Rhombus-free edge bound
Turan theorem
85
1
Triangular prism graph
Rhombus-free edge bound
32
Flow network
Graph theory
111
2
Max-flow min-cut theorem
Flow network
85
1
Parametric maximum flow with one source capacity
Max-flow min-cut theorem
40
Eulerian graph
Graph theory
54
1
Euler circuit criterion
Eulerian graph
41
Line graph
Graph theory
46
1
Line graph of a regular graph is Eulerian
Line graph
24
Planar graph
Graph theory
87
3
Euler formula for a connected planar graph
Planar graph
71
2
Planar graph edge bound
Euler formula for a connected planar graph
12
Planar girth edge bound
Euler formula for a connected planar graph
23
Crossing number
Graph theory
70
1
Crossing lemma
Crossing number
37
Graph neighbourhood
Graph theory
35
1
Common neighbour
Graph neighbourhood
14
Degree of a vertex
Graph theory
34
1
Locally finite graph
Degree of a vertex
11
Cut of a graph
Graph theory
180
5
Maximum cut
Cut of a graph
13
Unfriendly partition of a graph
Cut of a graph
143
3
Unfriendly partition theorem for a finite graph
Unfriendly partition of a graph
32
Unfriendly partition theorem for a countable locally finite graph
Unfriendly partition of a graph
40
Random unfriendly partition of a countable infinite-degree graph
Unfriendly partition of a graph
48
Bipartite graph
Graph theory
60
2
Complete bipartite graph
Bipartite graph
21
Two-colourability criterion for bipartite graphs
Bipartite graph
20
Directed graph
Graph theory
108
4
Directed edge
Directed graph
16
Directed walk
Directed graph
33
1
Closed directed walk
Directed walk
12
Adjacency matrix of a directed graph
Directed graph
49
Adjacency matrix of a graph
Graph theory
54
1
Walk count from powers of an adjacency matrix
Adjacency matrix of a graph
35
Graph distance
Graph theory
74
2
Graph diameter
Graph distance
59
1
Linear independence of adjacency powers up to the diameter
Graph diameter
45
Graph eigenvalue
Graph theory
13
Bipartite adjacency matrix
Graph theory
47
1
Perfect matching from a nonzero determinant
Bipartite adjacency matrix
32
Matching in a graph
Graph theory
227
8
Perfect matching
Matching in a graph
9
Maximal matching
Matching in a graph
37
Matching number
Matching in a graph
16
Hall marriage theorem
Matching in a graph
78
2
Hall induction through a tight set
Hall marriage theorem
39
Regular bipartite graph has a perfect matching
Hall marriage theorem
23
Regular-graph matching bound from unmatched vertices
Matching in a graph
58
1
Disjoint union of triangles as a sharp matching example
Regular-graph matching bound from unmatched vertices
25
Antichain
Graph theory
13
Ramsey theorem
Graph theory
239
8
Diagonal Ramsey number
Ramsey theorem
34
1
Binomial upper bound for a Ramsey number
Diagonal Ramsey number
13
Graph Ramsey number
Ramsey theorem
191
5
Off-diagonal graph Ramsey number
Graph Ramsey number
44
1
Clique-path Ramsey number
Off-diagonal graph Ramsey number
16
Ramsey number of a star
Graph Ramsey number
31
Paw graph
Graph Ramsey number
72
1
Ramsey number of the paw graph
Paw graph
62
Dirac theorem
Graph theory
15
Longest-path rotation
Graph theory
109
1
Neighbourhood bound for a square-free bipartite graph
Longest-path rotation
61
Strongly regular graph
Graph theory
17
Moser spindle
Graph theory
12
Random graph
Graph theory
287
8
Isolated vertex
Random graph
6
Erdős-Rényi model
Random graph
268
6
Isolated vertices in the Erdős-Rényi model
Erdős-Rényi model
75
1
Isolated-vertex threshold in the Erdős-Rényi model
Isolated vertices in the Erdős-Rényi model
40
Connectivity threshold in the Erdős-Rényi model
Erdős-Rényi model
44
Expected subgraph count in the Erdős-Rényi model
Erdős-Rényi model
131
2
Sparse clique-count concentration
Expected subgraph count in the Erdős-Rényi model
48
Vertex-disjoint sparse clique copies
Expected subgraph count in the Erdős-Rényi model
43
Complement graph
Graph theory
24
Menger theorem
Graph theory
239
10
Vertex separator
Menger theorem
26
Internally vertex-disjoint paths
Menger theorem
13
Set version of Menger theorem
Menger theorem
29
Linked graph
Menger theorem
26
Vertex connectivity
Menger theorem
64
2
Dirac circumference theorem
Vertex connectivity
43
1
Longest-cycle attachment argument
Dirac circumference theorem
30
Edge connectivity
Menger theorem
14
Whitney inequalities for graph connectivity
Menger theorem
37
1
Connectivity realization construction
Whitney inequalities for graph connectivity
31
Bipartite vertex cover
Graph theory
16
Ancestors
(4)
Foundations of mathematics
Area of mathematics
Mathematics
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