First thing : it is Karttikeya. Double t, and it comes from Krittika. The other spellings, Kartikeya and Karthikeya, can be condoned as common errors. Similarly the name Shanmuga comes from Shat-mukha (six heads), and SaravaNan comes from Sharavana-bhava ( meaning one born in a forest of shara grass).
This interesting deity is the darling of people from the South, with many lovely temples and rituals. Every Tamilian home has a Murugan (aaru-muga) picture day wall-calendar and many articles especially cloth-bags with the word Murugan.
This Hindu god is unique. He combines masculine valour, a boyish precociousness and also grace. He is in fact the military chief of the gods, and is considered the God of War, like Mars in Greek mythology (devasenapati). He is esoteric, and hence called "Guha', living in forested hills.
There are several Carnatic compositions of Muthuswami Dikshitar whose chosen deity was Guruguha or Karttikeya. But my favourite is the Todi piece Karttikeya Gangeya Gauri Tanaya, by Papanasam Sivan. It is a majestic composition with alliterative beauty, metrical grandeur, lyrical profundity, and to cap it all, the musical element does, in my opinion, justice to this unique raga which is a challenge to any musician, especially a vocalist. It is a raga that plumbs the depths of the lower notes and sets up edifices at Ga and Ma, with lovely glides along other notes. Somewhat like the glorious mountain peaks inhabited by Karttikeya, with delightful valleys and rivers. The above picture from an Internet website is charming in many dimensions.
Did you know that Karttikeya was born out of the fire, and nourished by Ganga, and breast-fed by six celestial deities called Krittikas (the star cluster)? And in only one stream of mythology was he born of Gauri as Kumara, in the story so well told by Kalidasa in Kumarasambhavam. The rest of the iconography showing him as the younger brother of Ganesha etc. is of popular value.
That Karttikeya is worshipped by forest and mountain dwellers is appropriate, and in all probablity he was the earliest male god in the Hindu pantheon, stemming from early man's idolatry of young war heroes.
Here are links to two great renderings of the Todi masterpiece:
M.S. Subbulakshmi
Lalgudi G. Jayaraman
Now, let me show you the entry under Karttikeya in A Classical Dictionary of Hindu Mythology and Religion by John Dowson, published first sometime about the middle of the 19th century and quite well-researched, like most European compilations (for that matter the most authoritative dictionary of Sanskrit is by Sir Monier Williams, as much as other Indian language reference dictionaries are by European scholars!)
So let us join in worshipping this wonderful deity, Karttikeya!