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I was wondering if anyone could provide references on the following: Is determining the chromatic number of a bounded degree graph APX-complete? 2.I've seen the result that states it is NP-hard t …

I'm interested in knowing if finding the edge-chromatic number of a $k$-uniform $k$-partite hypergraph is NP-hard for $k\geq 3$ Could anyone provide a reference for the result? By edge-chromatic numbe …

I have already asked one question on colouring, this question is more specific. Given a bounded degree graph $G$ with $\Delta(G)=2d$, is there a well know algorithm to achieve an approximation ratio …

I'm fairly new to colourings on bounded degree graphs i'm interested in the following questions, For planar graphs with bounded degree $4$ is finding the colouring number $NP$-hard? So is essential …

I'm interested to know whether the following problem is NP-complete or if there is an algorithm to solve it. Suppose we are given a directed graph $G=(V,E^{\rightarrow})$ and we want to colour the e …

I'm interested in orthogonal embeddings of graphs into the 2-dimensional, i.e where vertices are placed at integer co-ordinates and edges are routed along the grid lines and are not allowed to interse …

I'm interested in the following paper http://www.computer.org/csdl/trans/tc/1981/02/06312176.pdf In particular i'm interested in the construction Valiant describes to prove that it is possible to em …

In the following paper by Valiant http://www.computer.org/csdl/trans/tc/1981/02/06312176.pdf He shows under theorem 2 (at the bottom of the second page) that any planar graph $G$ of degree 3 or 4 w …

I'm reading the following paper on universality considerations in VLSI circuits http://www.computer.org/csdl/trans/tc/1981/02/06312176.pdf In Theorem 2 On the second page it states there exists cons …

I've seen the following lemma in a paper. The result is by Valiant. A planar graph $G$ with maximum degree $4$ can be embedded in the plane using $O(|V|)$ area in such a way that its vertices are at …

Suppose i have an $n \times n$ random bipartite graph and suppose that i repeat the following process $n$ times. At the start (stage 1) each edge is selected independently with probability $p(n)$, and …

Given a graph $G=(V,E)$ and a fixed integer $k$ are there any algorithms known which would find the maximum number of edge-disjoint cycles of length $k$ in $G$? If not is there a proof that this probl …

I've been told recently that it's better i just for help regarding my 'specific' problem rather than lots of little questions around the same topic which appear somewhat unclear. I would first like to …

Consider a random bipartite graph constructed on vertex classes of size $n$ with each edge present independently with probability $p$. How could I go about calculating the size of the expected matchin …

I'm defining the Hamming graph $H(d,q)$ in the usual way, so we have a set $S$ of $q$ elements, the hamming graph $H(d,q)$ has vertex set $S^{d}$ (the set of all ordered $d$-tuples of elements of $S$) …