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 )∪E(Q_2 )∪....∪E(Q


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

$L e t G b e a c o n n e c t e d g r a p h a n d l e t X b e t h e s e t o f v e r t i c e s o f G o f o d d d e g r e e . s u p p o s e t h a t ∣ X ∣= 2 k, w h e r e k ⩾ 1$ $s h o w t h a t t h e r e a r e k e d g e - d i s j o i n t t r a i l Q_{1}, Q_{2}, . . ., Q_{k} i n G s u c h t h a t$ $E (G) = E (Q_{1}) \cup E (Q_{2}) \cup . . . . \cup E (Q_{k})$
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