![](/files/happy5.png)
edge-coloring
Edge-antipodal colorings of cubes ★★
Author(s): Norine
We let denote the
-dimensional cube graph. A map
is called edge-antipodal if
whenever
are antipodal edges.
![$ d \ge 2 $](/files/tex/11eec08cccba2fc15cb1ab0db8568a42a91cced5.png)
![$ \phi : E(Q_d) \rightarrow \{0,1\} $](/files/tex/685e9db47a7cdebc035cdddc5627c69a11d93982.png)
![$ v,v' \in V(Q_d) $](/files/tex/7bdec5e833c3f44aaec5ec53ad5017b232be6354.png)
Keywords: antipodal; cube; edge-coloring
Goldberg's conjecture ★★★
Author(s): Goldberg
The overfull parameter is defined as follows:
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \chi'(G) \le \max\{ \Delta(G) + 1, w(G) \} $](/files/tex/688f47d207abb99bb15f8fc2353553cf3904fc1d.png)
Keywords: edge-coloring; multigraph
Seymour's r-graph conjecture ★★★
Author(s): Seymour
An -graph is an
-regular graph
with the property that
for every
with odd size.
![$ \chi'(G) \le r+1 $](/files/tex/efa38d9230a3451d1c38c061522cb607572d369b.png)
![$ r $](/files/tex/535dee6c3b72bcc4d571239ed00be162ee1e6fbe.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
Keywords: edge-coloring; r-graph
Monochromatic reachability or rainbow triangles ★★★
Author(s): Sands; Sauer; Woodrow
In an edge-colored digraph, we say that a subgraph is rainbow if all its edges have distinct colors, and monochromatic if all its edges have the same color.
![$ 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 $](/files/tex/d2b76a0ee5465d3e3ecc846c8e3d632edd8b2bbf.png)
Keywords: digraph; edge-coloring; tournament
Weak pentagon problem ★★
Author(s): Samal
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
Keywords: Clebsch graph; cut-continuous mapping; edge-coloring; homomorphism; pentagon
List colorings of edge-critical graphs ★★
Author(s): Mohar
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \Delta $](/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png)
![$ e $](/files/tex/5105762e0c97083905ebf07919c7d4d5ed38dce3.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ L(e) $](/files/tex/bd0dfc00a21966b9e90231c00dab0d0aa81a0ab0.png)
![$ \Delta $](/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ L $](/files/tex/73f33398d7e8aa42e6ec25ee2bb4f2b57ed3391a.png)
Keywords: edge-coloring; list coloring
A generalization of Vizing's Theorem? ★★
Author(s): Rosenfeld
![$ H $](/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png)
![$ d $](/files/tex/aeba4a4076fc495e8b5df04d874f2911a838883a.png)
![$ d-1 $](/files/tex/377f809b25769f204a72e5d4765cddd8aaabe392.png)
![$ r $](/files/tex/535dee6c3b72bcc4d571239ed00be162ee1e6fbe.png)
![$ r+d-1 $](/files/tex/43f812f49b2b3aee5d87139eaff0e0fe02c47dc8.png)
![$ d-1 $](/files/tex/377f809b25769f204a72e5d4765cddd8aaabe392.png)
Keywords: edge-coloring; hypergraph; Vizing
Partitioning edge-connectivity ★★
Author(s): DeVos
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ (a+b+2) $](/files/tex/af1c5eba58500364df6ff49bb0249ecfe43563fb.png)
![$ \{A,B\} $](/files/tex/b4558816c01c418eea76d970f1e3afdfd18e42d8.png)
![$ E(G) $](/files/tex/4b556e49b77160d4c8a0131e0efdfefd52dda2bb.png)
![$ (V,A) $](/files/tex/0682e0dcb16e4b0bfdebe28127ce935ebf4f792e.png)
![$ a $](/files/tex/b1d91efbd5571a84788303f1137fb33fe82c43e2.png)
![$ (V,B) $](/files/tex/a79aaba9b9fa199ba406f5d713827cda8507ed7c.png)
![$ b $](/files/tex/b94226d9717591da8122ae1467eda72a0f35d810.png)
Keywords: edge-coloring; edge-connectivity
Acyclic edge-colouring ★★
Author(s): Fiamcik
![$ \Delta $](/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png)
![$ (\Delta+2) $](/files/tex/6a77f06e08e0a0d164f09aa262634fe605297c08.png)
Keywords: edge-coloring
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