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Results tagged with graph-colorings
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user 9896
Vertex colouring, Edge Colouring, List Colouring, Fractional Chromatic Number and other variants of graph colouring problems are all on topic.
2
votes
1
answer
174
views
Bounds on chromatic index
Let $H$ be a hypergraph of maximum vertex-degree $\Delta$. (That is, for all vertices $x$, we have $| \{ e \in H \mid x \in e \} | \leq \Delta$) Are there any bounds on the chromatic index $\chi_e(H)$ …
- 3,475
7
votes
0
answers
214
views
Bound on chromatic number for a class of graphs
Consider a triangle-free graph $G$, in which the vertices are partitioned in blocks $V = A_1 \sqcup \dots \sqcup A_k$.
$G$ has the property that, for each $i \leq j$, each vertex in $A_i$ has at most …
- 3,475
5
votes
0
answers
148
views
Fractional chromatic number for triangle-free d-degenerate graphs
The following statement seems very plausible:
If $G$ is a triangle-free graph of degeneracy $d$, then
$$
\chi_f(G) \leq O(\frac{d}{\log d})
$$
where $\chi_f$ is the fractional chromatic number.
This …
- 3,475