Consider the sentence
Did you see the guy in red shirt?
Is it absolutely necessary to specify a shirt or the shirt?
Yes, sort of. A determiner, which includes articles, has to be there. Other classes include, possessive pronouns and nouns (e.g. my, your, John's) and demonstratives (e.g. this, that). Something, often an article, has to grant that shirt a sort of relative presence in the universe. Thus the red shirt, a red shirt, John's red shirt, that red shirt -- they all work. What does not work is red shirt with no word summarizing how it fits in the universe.
I understand that certain other languages do not require determiners. Or rather, context or some grammatical structure besides determiners accomplishes the same purpose. It is difficult to imagine a language which had no way of differentiating that red shirt from Tom's red shirt from any red shirt.
Inspired by Satnam's answer, let's look at plural nouns:
Do you see boys in red shirts?
Note that neither of the plural nouns has an obvious determiner. How can that be? It would appear English sometimes uses the context of plurality to apply an invisible or assumed determiner. The words any, the, and some would be good candidates. These vary in subtle ways:
Any vagueness of meaning could have been avoided by choosing actual determiners instead of leaving it to the listener or reader to decide. But if it doesn't matter to the author/speaker, so be it.
Yes your noun "shirt" in this sentence absolutely needs to have an article, either one would work depending on the context. The definite article is most likely what you want, but again that totally depends on context.
For example:
A policeman ran up, sweating heavily. "Did you see a guy in a red shirt?" he asked between breaths.
Indefinite article make the referenced noun (red shirt) less specific.
She looked at her friend and smiled. "Did you see the guy in the red shirt?" she asked mischievously.
Definite article makes the referenced noun (red shirt) very specific.
In your sentence, it is necessary to use either of the articles. MadGab explained very well the difference in usage of 'a
' and 'the
'. My answer is mostly concerning the use of the definitive article 'the
'.
When you say
Did you see the guy in the red shirt?
you are adding some information which is specific to the shirt the boy is wearing, i.e, it's red. In other words, you are talking about a particular shirt.
If you say,
Do you see the boys in red shirts?
putting 'the
' is optional as in this case, 'red shirts' is more of a general thing. If however, you choose to put 'the' in this sentence also, it would communicate that you are pointing to a particular 'group
' of shirts, all of which are 'red
'.