If they cannot, Chelsea will surely be waiting for them. This, too, is an inexperienced side but with the master title-winner Jose Mourinho - nine trophies since Wenger last won one - they will surely take advantage. Chelsea might not have Arsenal's depth or quality in central midfield, or their settled defence, or their capacity to control games, but they do have something else.
2. Will Manchester City sort out their away form?
It seems strange to discuss the title race without mentioning the best team in the league, but then this season's Manchester City are a very curious side.
City's top level, on their day and at home, is in a different category from every other team in the country. They have scored 25 goals in their last five games at the Etihad Stadium, and 44 in 11 this season. They put six past Tottenham and four past Manchester United in one of the best Premier League performances of recent seasons.
Maybe it should not be a surprise. City have the best strike force in the country. Alvaro Negredo has nine goals in his last seven games, Sergio Aguero has 12 in his last 10. Then there is the best box-to-box midfielder around in Yaya Touré, and two of the league's top creators - Samir Nasri and David Silva, who has not even been fit recently.
But the Premier League is a 38-game season and half of those games are away. And that is why City are already six points off the pace. For every brilliant home display there has been a poor one on the road, with performances that have been soft and careless in the extreme. City have already lost to Sunderland, Aston Villa and Cardiff City - not exactly the strongest opponents possible - as well as a poor draw at Stoke City and another defeat at Stamford Bridge.
Just as Manuel Pellegrini's thrilling 4-4-2 has delivered so much fun at home, the same system has left City exposed on the road. With Gareth Barry allowed to leave, there is no true holding player in midfield and far too much space in which opponents can attack. While Vincent Kompany struggles with muscle injuries, there is no leadership or authority in defence, although Martin Demichelis has introduced some experience into the backline.
Once this season, at Chelsea, Pellegrini abandoned his 4-4-2 to play 4-5-1 but City lost there and the experiment has not been repeated. But with trips to West Bromwich Albion, Southampton and Fulham this month, something will have to change to improve their away results, or else City may end up one of the finest non-champions of recent years.
3. Will United or Tottenham find the right combination?
The top three, though, is no closed shop and there are certainly teams outside it with the capacity to break in. The problem for Manchester United, Tottenham and Liverpool, however, is that until they settle on their strongest combination they will not be able to challenge the best.
This was always going to be a difficult season for United, as they attempted to replace the irreplaceable in Sir Alex Ferguson. David Moyes would need time to find his way into the job, and to learn about his players. However, the worry now in December is that it is not immediately obvious what his best midfield is, other than that it probably does not include £27.5m summer signing Marouane Fellaini. United's best recent performance, the 5-0 win at Bayer Leverkusen, was built around Phil Jones and Ryan Giggs but it is hard to see Moyes using the 40-year-old Giggs too often in the league.
Until there is a settled solution, though, and United start taking control of games in the middle, they might not be able to retain their title.
The problems at Tottenham are worse. Having sold one world-class player this summer - Gareth Bale -and bought seven good ones, teething problems were inevitable but Andre Villas-Boas still does not know his best system or his best team. Erik Lamela has started just one league game, while neither Roberto Soldado nor Christian Eriksen look particularly comfortable within the side. Even in December there are more questions than answers and until they are solved the manager will be under pressure.
Liverpool started stronger than either Spurs or United but they do not look like emerging from their long-term transition any time soon.
After a good spell with 3-5-2, the return to a back four - and the carousel of changing defenders - has seen them concede three in each of their last two games. With Daniel Sturridge injured there is still Luis Suarez but unless Brendan Rodgers can find a stronger base for his attacking players this will be another year outside the elite.
4. Can Everton, Newcastle or Southampton maintain their European challenge?
Early-season overachievers are often difficult to judge. Last year West Bromwich Albion looked like the year's big confounders, flying to third at this stage before eventually finding their level and finishing eighth. This year Everton have started better than expected, but the fringes of the top four are not new ground for them.
The big surprises, so far, have been Southampton and Newcastle United, clubs often mired in controversy because of their uncompromising owners, but who have, on the pitch, found a way of playing that has taken them above Manchester United and Tottenham.
Newcastle have been here before. They showed in 2011-12, when they finished fifth, that they can be a dangerous team. This year's side is slightly different; they do not have the roaming power of Demba Ba, but they do have the ruthless pace in behind defences of Loïc Rémy, and have now won four straight games, including the scalps of Chelsea and Tottenham. With no Europa League to stretch resources, they can hope to keep their first XI well settled. A repeat of two years ago is not inconceivable.
Southampton's situation is different. They have not finished in the top six of the top flight since 1985. But they are certainly upwardly mobile under Mauricio Pochettino who has built an energetic high-pressing team around a core of young English players. They have less firepower than Newcastle but are a better unit, and have the joint-best defensive record in the Premier League even after conceding three at Stamford Bridge on Sunday. Southampton boast less experience than Newcastle but more cohesion and might just outstay them at the business end of the table.
5. Will new managers (Poyet, Pulis and Meulensteen) inspire the bottom three?
Each of the bottom-three clubs have changed managers already, hoping that a quick switch will give enough time to improve results. Gus Poyet at Sunderland is the relative veteran, having overseen six games so far, two of which were rousing home wins over Newcastle United and Manchester City. The away results have been poor but he does have players who can score goals and, with 13 home games remaining, there should be just enough time for him to re-impose unity and make the difference required.
Fulham's Rene Meulensteen and Tony Pulis at Crystal Palace have harder jobs. Meulensteen must inject some energy and momentum into a team where both seem to have dissipated. He has some good technical players at his disposal but the problems at Craven Cottage look complex. This is a team that needs management as well as coaching - can Meulensteen conjure up some confidence and form?
Pulis, though, must wish he had Fulham's squad. Crystal Palace were the fifth-best team in the Championship last season and their summer transfer activity has not exactly brought a transformation. Pulis overachieved with a limited squad at Stoke City but he needs to do something very special with his new players, starting against West Ham this evening.
While the bottom three have changed managers, those just above them - not least Norwich City - must nervously wait to see what happens. Chris Hughton has not exactly justified his summer spending, and despite two wins in their last three games, their situation looks precarious. Along with West Ham and Stoke City, they could be vulnerable to any great surge from beneath.
