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.A G2/M arrest of mink cells infected with feline panleukopenia virus.
During feline panleukopenia virus (FPV) infection of mink, early signs of depression are associated with small cell aggregates of the nucleus and cytoplasm, which appear as rough-looking cells and which do not stain by the Romanowsky stains. When giant cells accumulate, the nucleus and cytoplasm are enlarged to form large cells which stain uniformly. Both cell types have the ability to continue to divide.Q:

Is this true statement, “difference in finding the longest path from two graphs $G_1$ and $G_2$ is bounded by $O(nm)$”

Let two weighted graphs $G_1$, $G_2$ such that $\vert G_1\vert=n, \vert G_2\vert=m$. Let $d_1$ be the length of the longest path in graph $G_1$ and $d_2$ be the length of the longest path in $G_2$. Let $d=\max(d_1,d_2)$.
The statement is,
$$\vert d(G_1,G_2)-d\vert \le O(nm).$$
I have problems to prove this statement. Can anyone help me in this problem?


Show that the longest path in a graph $G$ is of length $O(n\sqrt{V(G)})$.
Since $G$ has at least one node, we can assume $n\geq 1$. Consider the definition of $d$. If $d$ is the length of the longest path in $G$, then $d=\max\{d_1,d_2\}\geq\min\{d_1,d_2\}=d_1\ve

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‘RNZ Christchurch: a history of New Zealand’ by William A. S. Colwell (with art by J. Cameron. A library in Christchurch has a collection of De Pauw’s books which have been donated to it to mark the Centenary. (pg. 51-52) He concludes that this was the most complete library of its day in Europe and held an inventory of 280,000 items. (pg. 51) According to Colwell, De Pauw catalogued a great many of the books that came into the Christchurch library during the first few decades of the 19th century, and some of these books were added to his catalogue. (pg. 53) The University of Canterbury collection is bound in front of the list of items in his catalogue, demonstrating that De Pauw’s catalogue included these items. (pg. 52)
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