R

replaced - zamieniony

registration fee - opłata rejestracyjna

request - życzenie, prośba

regret  - żałować, ubolewać

refer to - powoływać się

carry the responsibility - ponosić odpowiedzialność

as a rule - w zasadzie (z reguły)

to have recourse to - uciekać się do

resulting in, result in - kończąc się, dawać w efekcie

to be referred to as a block - nazywana blokiem

rather then - zamiast

as a result of - w rezultacie

relating to - dotyczące

restrictions on - ograniczenia na

these must be reflected in restriction on the - musi to mieć swoje odbicie w ograniczeniach

it remains to show - pozostaje pokazać

than the remainder of the vertices are colored -

S-stage network to which we refer - S-sekcyjna sieć o której mówimy (którą mamy na myśli)

with respect to - z uwzględnieniem

this paper reports on a study of - artykuł ten poświęcony jest

this has been referred to as Benes' network - układ ten został nazwany układem Benes'a

thus the second alternative is ruled out - zatem druga możliwość jest wykluczona

reproduced  - przytoczony

The resultant graphs... -

the following  observations are required for the proof. -

in this respect - w tym względzie

entries made at random -

# is reduced by 2 - # jest zmniejszony o 2

to be regarded as  - być uważanym za ( traktowanym jako)

a relevant question is, which ...? - istotne jest pytanie...?

#1 is large relative to #2 -  #1 jest duże względem #2

in relation to - w stosunku do

The reason for maintaining this set will soon be made clear.

We recall that ... - przypominany , że

Regarding  the number of colours ... - biorąc pod uwagę liczbę kolorów...

Running times were  evaluated with a CPU times with a 1ms resolution

right angle - kąt  prosty

rational number   - liczba wymierna

resistance - oporność

rigidity - sztywność

rot - zgnicie, zepsucie

rotation - rotacja

directly related to -  bezpośrednio związany z

up until recently - do niedawna

ranging from #1 to #2  - o zasięgu od #1 do #2

While is appears that this higher order of growth is the minimum order of growth, no one has ever proved that the informational bound cannot be reached.

All that remains is to extend the coloring to ... - Pozostaje jedynie

with regard to - pod względem

with relation to - względem

A worse case example is constructed which requires this algorithm to perform O(n3) operations

repetition - iteracja

conditional repetition - warunkowa iterowalność

The reason for this is that the node coloring models enable us to incorporate a variety of constrains which cannot easily be introduced in a formulation based on edge coloring

refute - obalić (np. twierdzenie)

... then the ratio between... -

It is for this reason that ... -

Refraining from doublures like isomorphic partitions etc .., - powstrzymując się od ...

readily  - łatwo

The algorithms  rely on ...

The ranking function takes the following into account :

retain - zachowywać w pamięci

# are retained so as to avoid recomputing their values

the result for d=3 may be within reach, but for general dimension we know nothing -

But by religiously following the rules, we can ... - skrupulatnie

redo - ponownie wykonywać

reaplication - ponowne użycie

recast - przerobić

are retained so as to avoid recomputing their values

in the range [1,m] -

Polynomial time algorithms for solving this problem exist  only for very restrictive classes of graphs.

This question was raised by... -

the righthandside of (*) gives

By the same reasoning,... -

It is readily seen that... -

We ran 100 simulations for each n in the range n = 0-300, step size 60

Much research has been done on...

For graphs of genus g, Euler's formula reads m 3n+6(g-1)

# is interesting in  its own right

The remainder of the paper is organized as follows.

Let a = a (G) in the rest of the paper

The algorithm designer must then settle for less: either to relax the requirement that the algorithm be polynomial-time, as in the design of branch-and-bound algorithms, or to relax the requirement that the algorithm always deliver an optimal solution.

The proof of this result is reminiscent of the proof given above.

Although ... , I have several reservations about this paper.

Along the way, we will need to prove some new NP-completeness results for hypergraph colorings with are of interest in their own right.

to resort to computation - uciec się do obliczeń

The integer round - up of # - zaokrąglenie w górę do najbliższej liczby całkowitej

readable – czytelne

Further theoretical research is necessary to confirm or refute this conjecture.

..., we color the reinserted path with colors 1 and 2.