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Mathematical Problems of Computer Science 29, 2007, 16{20.

On Cyclically Continuous E dge Color ings of T r ees

R a fa ye l R . K a m a lia n

Institute for Informatics and Automation Problems of NAS of RA

e-mail: rrkamalian@yahoo.com

Abstract

A cyclically continuous edge coloring of a graph is de¯ned. For an arbitrary tree the
existence of this coloring is proved and all possible numbers of colors in such colorings
are found.

Refer ences

[1 ] F. H a r a r y, Gr a p h Th e o r y, A d d is o n -W e s le y, R e a d in g , MA , 1 9 6 9 .

[2 ] V iz in g V . G., " Th e c h r o m a t ic in d e x o f a m u lt ig r a p h " , ( in R u s s ia n ) , K ibernetika No.
3, K iev, p p . 2 9 -3 9 , 1 9 6 5 .

[3 ] R .R .K a m a lia n , In t e r va l E d g e Co lo u r in g s o f Gr a p h s , D o c t o r a l D is s e r t a t io n , In s t it u t e o f
Ma t h e m a t ic s o f t h e S ib e r ia n B r a n c h o f t h e A c a d e m y o f S c ie n c e s o f U S S R , N o vo s ib ir s k,
1 9 9 0 .

[4 ] A .S . A s r a t ia n , R .R .K a m a lia n , " In t e r va l e d g e c o lo u r in g o f m u lt ig r a p h s " , Appl. M ath.,
Yerevan Univ., vo l. 5 , p p . 2 5 -3 4 , 1 9 8 7 ,( in R u s s ia n ) .

[5 ] R .R .K a m a lia n , " In t e r va l c o lo u r in g s o f c o m p le t e b ip a r t it e g r a p h s a n d t r e e s " , ( in R u s -
s ia n ) , P reprint of the Computing Centre of the Academy of Sciences of Armenia, Yere-
van, 1 9 8 9 .

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