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digraph
Monochromatic reachability or rainbow triangles ★★★
Author(s): Sands; Sauer; Woodrow
In an edge-colored digraph, we say that a subgraph is rainbow if all its edges have distinct colors, and monochromatic if all its edges have the same color.
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ v $](/files/tex/96cbd9a16c6a5eab03815b093b08f3b2db614e9a.png)
![$ v $](/files/tex/96cbd9a16c6a5eab03815b093b08f3b2db614e9a.png)
Keywords: digraph; edge-coloring; tournament
Monochromatic reachability in edge-colored tournaments ★★★
Author(s): Erdos
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ f(n) $](/files/tex/9579fe06c51fc31a993cd148e8bbc3cb07df464e.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ S $](/files/tex/d2b76a0ee5465d3e3ecc846c8e3d632edd8b2bbf.png)
![$ f(n) $](/files/tex/9579fe06c51fc31a993cd148e8bbc3cb07df464e.png)
![$ S $](/files/tex/d2b76a0ee5465d3e3ecc846c8e3d632edd8b2bbf.png)
Keywords: digraph; edge-coloring; tournament
Non-edges vs. feedback edge sets in digraphs ★★★
Author(s): Chudnovsky; Seymour; Sullivan
For any simple digraph , we let
be the number of unordered pairs of nonadjacent vertices (i.e. the number of non-edges), and
be the size of the smallest feedback edge set.
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \le 3 $](/files/tex/2dbc994c29a8272f2fa20bee6216f47315c47aa7.png)
![$ \beta(G) \le \frac{1}{2} \gamma(G) $](/files/tex/d2838535a0339a448fba3bbbab8586020be5f886.png)
Keywords: acyclic; digraph; feedback edge set; triangle free
Highly arc transitive two ended digraphs ★★
Author(s): Cameron; Praeger; Wormald
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
Keywords: arc transitive; digraph; infinite graph
Universal highly arc transitive digraphs ★★★
Author(s): Cameron; Praeger; Wormald
An alternating walk in a digraph is a walk so that the vertex
is either the head of both
and
or the tail of both
and
for every
. A digraph is universal if for every pair of edges
, there is an alternating walk containing both
and
Keywords: arc transitive; digraph
Woodall's Conjecture ★★★
Author(s): Woodall
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
The Two Color Conjecture ★★
Author(s): Neumann-Lara
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ V(G) $](/files/tex/b324b54d8674fa66eb7e616b03c7a601ccdab6b8.png)
![$ \{X_1,X_2\} $](/files/tex/1ac50179d3c46ba43d2b8183a945de84c223f351.png)
![$ X_i $](/files/tex/4d0fffaf276df9eeca81fca1efb9e42157b0a9f9.png)
![$ i=1,2 $](/files/tex/1db9f0079a9ca23741381d2fbc830c48d730c458.png)
![Syndicate content Syndicate content](/misc/feed.png)