# triangle free

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

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

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

## Non-edges vs. feedback edge sets in digraphs ★★★

Author(s): Chudnovsky; Seymour; Sullivan

For any simple digraph , we let be the number of unordered pairs of nonadjacent vertices (i.e. the number of non-edges), and be the size of the smallest feedback edge set.

**Conjecture**If is a simple digraph without directed cycles of length , then .

Keywords: acyclic; digraph; feedback edge set; triangle free

## Circular coloring triangle-free subcubic planar graphs ★★

**Problem**Does every triangle-free planar graph of maximum degree three have circular chromatic number at most ?

Keywords: circular coloring; planar graph; triangle free

## Unions of triangle free graphs ★★★

**Problem**Does there exist a graph with no subgraph isomorphic to which cannot be expressed as a union of triangle free graphs?

Keywords: forbidden subgraph; infinite graph; triangle free

## Triangle free strongly regular graphs ★★★

Author(s):

**Problem**Is there an eighth triangle free strongly regular graph?

Keywords: strongly regular; triangle free