That's it from me.
If you want to read more on Arsenal's win, follow this link.
And you can follow all the reaction from Monday's Premier League games here.
Happy new year to you all.
That's it. Arsenal go top of the Premier League, for 24 hours at least.
Bournemouth have kept on going and Glenn Murray puts a dangerous strike across goal, which Petr Cech finger-tips wide.
But straight on the counter attack go Arsenal. Mesut Ozil once again supplies Theo Walcott but the England man can only force a save from Artur Boruc.
Another mazy run from Alex Oxlade-Chamberlain sees him make it into the box, but he's hustled out by the Bournemouth defence.
Mesut Ozil then swings in a sumptuous pass for Theo Walcott, but the Arsenal forward can't convert.
Alex Oxlade-Chamberlain is inches away from Arsenal's third.
He cuts inside and his shot is just deflected wide of the post.
At the other end, Junior Stanislas controls the ball and attempts to unnerve goalkeeper Petr Cech with a cross-shot, but it's wide.
Eunan O'Kane has a go from inside the box for Bournemouth but it goes pretty high over the target.
Another change for Arsenal as Nacho Monreal comes on for Kieran Gibbs.
Bournemouth forward Joshua King doesn't look too peachy. He's pulled up with a hamstring injury and is replaced by Glenn Murray.
Meanwhile, Olivier Giroud slices wide of the target and is then replaced himself by Joel Campbell.
If Bournemouth fail to score, there's a Premier League record heading Petr Cech's way.
The Arsenal goalkeeper will have kept his 170th top-flight clean sheet. Quite remarkable.
Still 15 minutes to go, mind.
Bournemouth are still having a go here.
Winger Matt Ritchie lets fly from 30 yards but his shot is caught by goalkeeper Petr Cech.
Close again for the hosts. Olivier Giroud's shot is saved by Artur Boruc and parries the ball into the path of Theo Walcott, but he misses and he's then ruled offside anyway.
Two Arsenal chances go a begging in quick succession.
First Olivier Giroud is unable to control Aaron Ramsey's pull-back and although Bournemouth clear the danger, Mesut Ozil finds himself in space again.
The German can't find anyone to feed to, though.
BBC Sport at Emirates Stadium
"The first 'we are top of the league' chant rings out around Emirates Stadium, and the pressure is back on Leicester tomorrow night as the Gunners look set to reclaim top spot tonight. Bournemouth will hustle and bustle, but realistically it looks like damage limitation for the Cherries from now."
Another beautiful Arsenal break.
Hector Bellerin feeds Theo Walcott and the England man hits it low but puts it just past the post.
Some slick, slick action on show from Arsenal for their second.
Mesut Ozil passes to Olivier Giroud, and the Frenchman, with his back to goal, provides a cute flick for Ozil to casually slot home.
Cool as you like.
Dan Gosling is looking fairly lively for the visitors.
The midfielder meanders his way into the box and grapples with goal-scorer Gabriel, and the ball is cleared.
But it's to be Gosling's last action of the match. He comes off and Eunan O'Kane takes his place.
Meanwhile, Calum Chambers is booked for a challenge on Harry Arter .
Arsenal have switched off a bit and Bournemouth earn a corner.
Cherries substitute Junior Stanislas takes it short to Harry Arter, and the ball is flung in but Calum Chambers rises high to head away the danger.
Petr Cech sees some action! The Arsenal goalkeeper collects Adam Smith's ball from the right with ease, after some nice overlap play from Smith and Matt Ritchie.
Bournemouth play a diagonal ball across to lone striker Joshua King, who looks offside and even has a look himself. He pulls the ball back to Junior Stanislas but the danger is expertly cleared by Gabriel.
Theo Walcott immediately goes on the break and Bournemouth manage to halt the pressure, but only after Alex Oxlade-Chamberlain's deflected shot is collected by goalkeeper Artur Boruc.
Off we go, then.
Bournemouth start us off again, kicking left to right.
The players filter back out onto the immaculate Emirates pitch.
Bournemouth make one change as Junior Stanislas comes on for Marc Pugh on the left-hand side. A straight swap from Eddie Howe.
It's pretty clear to see who Arsenal's danger man is.
Mesut Ozil has taken 55 touches in the first half, completed eight crosses, and made six key passes in attack - all of which are game-high tallies.
And he's now up to 16 assists for the season, too.
The stats at half-time show Arsenal's dominance, despite a really decent opening 15 minutes from Bournemouth.
Arsenal end the half in the ascendancy but can't find a second goal...yet.
Referee Roger East waves away Arsenal calls for a penalty, as Olivier Giroud feels he was impeded by Simon Francis but it was the Gunners man who backed up into Francis.
The half-time whistle goes and Bournemouth have got a tough job on their hands.
Bournemouth are having to defend very,very deep while Arsenal casually pass the ball around with ease.
Hector Bellerin launches three separate crosses in from the right, and although none of them are met by a waiting Arsenal forward, it's keeping the Cherries defence on their toes.
Then, from a Mesut Ozil corner, Aaron Ramsey comes storming in but his header goes away from the goal.
It's all Arsenal now.
Alex Oxlade-Chamberlain makes headway on the right flank, and a beautiful Mesut Ozil ball to Theo Walcott isn't converted.
And then, somehow, Per Mertesacker manages to head against the side of the post from about two yards out.
To be fair to the German, he didn't know much about it. Gabriel's shot had come off the post and it was palmed in his direction by Bournemouth goalkeeper Artur Boruc.
BBC Sport at Emirates Stadium
"This time there was no mistake from Arsenal's set-piece technique as Gabriel escaped his marker to meet Ozil's sweetly struck corner with a firm header across Boruc's goal. Suddenly the tension of the preceding few minutes disappears - and the Gunners are back on track to top the league, at least for the next 24 hours."
A lovely run from Alex Oxlade-Chamberlain forces a corner. It's whipped in by Mesut Ozil and headed in beautifully by defender Gabriel for his first Arsenal goal.
Harsh on Bournemouth, but well executed by the hosts.
Ooooh, we've got some groans from the Arsenal fans.
"Come on!", you can hear them shout.
And their calls work. Arsenal's first real chance comes as Mesut Ozil dinks a ball over the defence and finds Theo Walcott, but he fails to connect and it's collected by keeper Artur Boruc.
I won't lie, this game isn't great so far.
It's very pedestrian from both sides - no-one's really broken a sweat.
Hector Bellerin fouls Bournemouth's Marc Pugh and gives away a free-kick but it comes to nothing.
At the other end, Calum Chambers tries to swing a ball across the box from the right but it's wayward.
BBC Sport at Emirates Stadium
"Bournemouth manager Eddie Howe singled out their defending of set-pieces for praise after Boxing Day's goalless draw with Crystal Palace, and his goalkeeper Artur Boruc will be happy if all Arsenal's corners are like their first, floated in and allowing him to catch the ball unchallenged. While the visitors have had to stand firm in defence so far, a wide, well-manicured pitch has allowed them some dangerous breaks upfield against the would-be league leaders."
Bournemouth aren't scared to have a go.
An accurate ball-in from Harry Arter finds striker Joshua King but he's smothered under a pile of Arsenal defenders.
Arsenal midfielder Alex Oxlade-Chamberlain goes on the attack before being clipped on the ankle and brought down.
Arsenal haven't got to grips with the game just yet, but are able to produce a nifty little counter-attack.
Aaron Ramsey snatches a loose ball in midfield and it's fed out wide on the left but Olivier Giroud can't find Mesut Ozil and it's cleared.