# Reed, Bruce A.

## Forcing a 2-regular minor ★★

Author(s): Reed; Wood

Conjecture   Every graph with average degree at least contains every 2-regular graph on vertices as a minor.

Keywords: minors

Author(s): Harvey; Reed; Seymour; Wood

Conjecture   For every graph ,
(a)
(b)
(c) .

Keywords: fractional coloring, minors

## Weighted colouring of hexagonal graphs. ★★

Author(s): McDiarmid; Reed

Conjecture   There is an absolute constant such that for every hexagonal graph and vertex weighting ,

Keywords:

## Hoàng-Reed Conjecture ★★★

Author(s): Hoang; Reed

Conjecture   Every digraph in which each vertex has outdegree at least contains directed cycles such that meets in at most one vertex, .

Keywords:

## Antidirected trees in digraphs ★★

Author(s): Addario-Berry; Havet; Linhares Sales; Reed; Thomassé

An antidirected tree is an orientation of a tree in which every vertex has either indegree 0 or outdergree 0.

Conjecture   Let be a digraph. If , then contains every antidirected tree of order .

Keywords:

## Domination in cubic graphs ★★

Author(s): Reed

Problem   Does every 3-connected cubic graph satisfy ?

Keywords: cubic graph; domination

## Bounding the chromatic number of triangle-free graphs with fixed maximum degree ★★

Author(s): Kostochka; Reed

Conjecture   A triangle-free graph with maximum degree has chromatic number at most .

Keywords: chromatic number; girth; maximum degree; triangle free

## Reed's omega, delta, and chi conjecture ★★★

Author(s): Reed

For a graph , we define to be the maximum degree, to be the size of the largest clique subgraph, and to be the chromatic number of .

Conjecture   for every graph .

Keywords: coloring