Let-G-be-a-connected-graph-and-let-X-be-the-set-of-vertices-of-G-of-odd-degree-suppose-that-X-2k-where-k-1-show-that-there-are-k-edge-disjoint-trail-Q-1-Q-2-Q-k-in-G-such-that-E-G-E-Q-1-

Question Number 94419 by sorour87.d last updated on 18/May/20

L e t G b e a c o n n e c t e d g r a p h a n d l e t X b e t h e s e t o f v e r t i c e s o f G o f o d d d e g r e e . s u p p o s e t h a t ∣ X ∣= 2 k, w h e r e k ⩾ 1

s h o w t h a t t h e r e a r e k e d g e - d i s j o i n t t r a i l Q_{1}, Q_{2}, \dots, Q_{k} i n G s u c h t h a t

E (G) = E (Q_{1}) \cup E (Q_{2}) \cup \dots . \cup E (Q_{k})