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{{unsolved|mathematics|Which finite groups are BI-groups?}} ...ó Babai|title=Spectra of Cayley graphs |journal=[[Journal of Combinatorial Theory, Series B]] |date=October 1979 |volume=27 |issue=2 |pages=180–189 |doi=10.1 ...

...The problem asks whether a given list of pairs can be used to construct a graph, and for the list above, the answer is yes.]] ...v_i</math> has [[directed graph|indegree]] <math>a_i</math> and [[directed graph|outdegree]] <math>b_i</math>. ...

{{unsolved|mathematics|Does forbidding both a tree and a clique as induced subgraphs p ...either <math>T</math> nor <math>K</math> as [[induced subgraph]]s can be [[graph coloring|properly colored]] using only a constant number of colors. Equival ...

{{Short description|Existence of a graph with a degree sequence}} ...such that <math>(d_1,\dots,d_n)</math> is the [[degree sequence]] of this graph. ...

{{Short description|On existence of a strongly regular graph}} {{unsolved|mathematics|Does there exist a [[strongly regular graph]] with parameters (99,14,1,2)?}} ...

{{Short description|Unsolved problem about oriented graphs}} ...rk on the Second Neighborhood Problem |journal=Electronic Journal of Graph Theory and Applications |year=2015 |volume=3 |issue=2 |pages=182–190 |doi=10.5614/ ...

{{Short description|Finding the largest graph of given diameter and degree}} ...cs|Given two positive integers {{mvar|d}}, {{mvar|k}}, what is the largest graph of diameter {{mvar|k}} such that all vertices have degrees at most {{mvar|d ...

...nal|last1=Friedgut|first1=Ehud|last2=Kalai|first2=Gil|title=Every monotone graph property has a sharp threshold|journal=Proceedings of the American Mathemat ...= \sum_{S \subset [n]} \widehat{f}(S) x_S, \text{ where } x_S = \prod_{i \in S} x_i. </math> ...

...the [[bipartite graph]] below it, where each vertex has a [[degree (graph theory)|degree]] equal to the number assigned to it.]] ...s,b_m)</math> is the [[bipartite graph|degree sequence]] of this bipartite graph. ...

...he first graph is connected by exactly one path of length 1, and each pair in the second is connected by one of length 2. These are the cases <math>k = 1 {{unsolved|mathematics|Is there a finite graph on at least two vertices in which each pair of distinct vertices is connected by ''exactly one'' path o ...

{{unsolved|mathematics|Do minor-closed graph families have <math>\ell_1</math> embeddings with bounded distortion?}} ...Ilan Newman, Yuri Rabinovich, and [[Alistair Sinclair]], who formulated it in 2004.{{r|gnrs}} ...

{{Short description|Unsolved problem in graph theory}} ...dean plane]]. It was proposed by [[Edgar Gilbert]] and [[Henry O. Pollak]] in 1968.<ref>{{Cite journal|last1=Gilbert|first1=E. N.|last2=Pollak|first2=H. ...

...[[Laplacian matrix|Laplacian]] of a [[graph (discrete mathematics)|graph]] in term of its number of edges.<ref name=":0">{{Cite book|last1=Brouwer|first1 The conjecture states that if ''G'' is a simple undirected graph and ''L''(''G'') its Laplacian matrix, then its eigenvalues ''λ''<sub>''n'' ...

{{unsolved|mathematics|Is there a [[dense set]] of points in the plane at rational distances from each other?}} In [[mathematics]], the '''Erdős–Ulam problem''' asks whether the plane contai ...

{{Short description|Unsolved problem in parallel algorithms}} ...ph connectivity]]. The input to the problem is a [[regular graph|2-regular graph]], forming either a single connected <math>n</math>-vertex cycle or two dis ...

[[File:Rhombic dodecahedron linear arboricity.svg|thumb|Partition of the graph of a [[rhombic dodecahedron]] into two [[linear forest]]s, showing that its ...city is a variant of [[arboricity]], the minimum number of [[forest (graph theory)|forest]]s into which the edges can be partitioned. ...

{{Short description|Problem on triangles in graph theory}} ...e blue and yellow vertex coloring). According to Tuza's conjecture, in any graph, it is possible to remove twice as many edges as the maximum triangle packi ...

{{Short description|Unsolved problem in discrete geometry}} ...f ten points, but have no big line (the largest collinear subset of points in convex position has only two points). According to the big-line-big-clique ...

...ommonly denoted <math>\chi(G)</math>. An overview of the area can be found in a survey of Alex Scott and [[Paul Seymour (mathematician)|Paul Seymour]].{{ ...|1949}} and {{harvtxt|Mycielski|1955}} showed, there exist [[triangle-free graph]]s of arbitrarily large chromatic number,{{r|descartes|z|m}} so for these g ...

{{short description|Relation between graph coloring and crossings}} ...Do [[complete graph]]s have the smallest possible [[Crossing number (graph theory)|crossing number]] among graphs with the same [[chromatic number]]?}} ...