Röstigraben is something to do with the culture of Switzerland‘s German and French speaking peoples.
Indeed.
Rösti, which means literally roast (of potatoes) is the German Swiss national dish and is actually the traditional farmers breakfast. You go out at 5 o'clock and -20 C to milk the cows in winter...
The Röstigraben 'the rösti ditch' describes the divide between the German and the French speaking parts of the country, politically as well as culturally and not just the language. The German part tends to be traditionally more conservative while the French part is generally more liberal, for instance. And of course the languages also connect us with our neighbouring countries which we have close local connections to.
Being a multi-lingual country has very much its own challenges. The UK is comprised of several whole nations plus smaller dependencies. Switzerland only comprises small parts of several neighbouring nations but it has in many ways taken the opposite approach to the UK: very much from the grassroots up (the most direct democracy) and it is held together by deliberate choice of wanting to be part of a Swiss nation (initially a coalition of cantons) and not the country whose language you share. However, finding the famous Swiss compromise (nobody is happy but everybody can live with the result) can be very challenging; especially when the two largest blocks, the German and the French speaking parts of Switzerland don't see eye to eye on many issues. Political representation is an essential tool of Swiss politics so the majority of voters is representated from parliament up right into the government of 7 ministers, of which two have to be French speakers. It is also compromised of the 4 largest political parties, so who gets into the government has to be both from the right party as well as the right part of the country... It makes for stability but leadership in a fast moving crisis can be weak, as the pandemic has shown.
The divide between the German and the Italian speaking part south of the Alps (about 10% of the population) is called the polenta ditch after the main dish of the Italian speaking population. The French and Italian parts don't have much of a shared border as they are basically Alpine valleys. The fourth national language, Romansh, is only spoken in a very few Alpine valleys in the Southeast by about half a percent of the overall population.
My friends who grew up on the German/French border use both languages but it depends on the context and not so much the people as to which one they use. German is better for facts and organisation. Emotional concepts and situations happen in French.
PS: Here is how a proper Swiss roesti is made. It does nicely silence a room! It's still one of my favourite dished. Ask
@Claire W - she's had quite a few rösti dinners over the years!
Rösti - Wikipedia