yes
The deadly fight between Romeo and Tybalt was not inevitable. It was a result of a series of misunderstandings and impulsiveness on both sides. If they had taken a moment to think rationally or if circumstances had been different, the fight could have been avoided.
Tybalt was asking for a fight with Romeo. Since he was married to Juliet and Tybalt was now his cousin, he refused to fight him. Then Mercutio asked to fight Tybalt and in a way kind of tempted him to fighting. Tybalt ended up killing Mercutio because Romeo got in the way when trying to stop the fight between the two. So now Romeo is angry that his friend Mercutio is dead and Tybalt doesn't have a scratch. So, Tybalt and Romeo fight and Romeo kills Tybalt.
The immediate outcome of the fight between Romeo and Tybalt was that Romeo won and Tybalt died. This had the effect of getting Romeo banished from Verona.
earlier in the play, romeo crashed a Capulet party. angry, Tybalt swore revenge with a sword fight. Romeo's friend mercutio ends up fighting Tybalt, and romeo attempts to intervene by stepping between them. Tybalt stabs mercutio, despite Romeos attempts to end the fight, and mercutio dies. Romeo and Tybalt then fight, and romeo kills Tybalt, and romeo is banished from Vienna. Merutio, romeo and Tybalt sword fight.
The devil is to blame. Really.
Mercutio is the one who decides to fight Tybalt.
The fight between Tybalt and Romeo takes place in Act 3 scene 1 lines 113-121 (Cambridge Schools Shakespeare)
Tybalt insults Romeo by calling him a "villain." He also provokes him by questioning his presence at the Capulet party and by criticizing his behavior towards Juliet. This ultimately leads to a fight between them.
Tybalt wants to fight him. Tybalt always wants to fight someone, and he has fastened on Romeo after Tybalt spotted him at the party in Act I Scene 5.
Romeo refuses to fight Tybalt. Mercutio steps in for Romeo and fights Tybalt. Romeo steps between them, trying to stop the fight. Tybalt stabs Mercutio. Mercutio curses both the Capulets and Montagues. Mercutio dies. Romeo is enraged and decides to fight Tybalt. Romeo kills Tybalt, then he runs. Prince Escalus comes to the scene. He announces Romeo's banishment.
At first, Romeo does not want to fight with Tybalt because he is now married to his kinswoman, Juliet. This makes Romeo and Tybalt of the same family, and Romeo does not want to fight his own.
Basically they were spoiling for a fight. Tybalt was looking for Romeo in order to fight him, but Romeo didn't want to fight Tybalt. Mercutio didn't like Tybalt at all and was looking for a chance to fight him. He used the situation as a pretext to challenge Tybalt, who was not a man to turn down anyone's challenge.
Romeo kills Tybalt.