Chen, Wei-Guo

Chen, Zhi-Hong

Luo, Weiqi

English

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Butler University Digital Commons @ Butler University Scholarship and Professional Work - LAS College of Liberal Arts & Sciences 7-2014 Edge-connectivities for spanning trails with prescribed edges Wei-Guo Chen Zhi-Hong Chen Butler University, chen@butler.edu Weiqi Luo Follow this and additional works at: https://digitalcommons.butler.edu/facsch_papers  Part of the Computer Sciences Commons, and the Mathematics Commons Recommended Citation Chen, Wei-Guo; Chen, Zhi-Hong; and Luo, Weiqi, "Edge-connectivities for spanning trails with prescribed edges" Ars Combinatoria / (2014): 175-186. Available at https://digitalcommons.butler.edu/facsch_papers/1047 This Article is brought to you for free and open access by the College of Liberal Arts & Sciences at Digital Commons @ Butler University. It has been accepted for inclusion in Scholarship and Professional Work - LAS by an authorized administrator of Digital Commons @ Butler University. For more information, please contact digitalscholarship@butler.edu. ----·---------- ----�---- --- - --- - ------- -Edge-connectivities for spanning trails with prescribed edges Wei-Guo, Chen Guangdong Information Center, Guangzhou, P_ R. China Zhi-Hong Chen * Butler University, Indianapolis, IN 46208 Weiqi Luo JiNan University, Guangzhou, P_R. China June 5, 2009 Abstract For a graph G, a vertex-edge alternating sequence vo, e1, v1, e2, • -ek-I,Vk-1,ek,vk such that all the ei's are distinct and ei = Vi-iVi for all i is called a trail. For u, v E V(G), a (u, v)-trail of G is a trail in G whose origin is u and whose terminus is v. A (u, v) trail is called a close trail if u = v. A trail H is called a spanning trail of a graph G if V(H) = V(G)_ Let X,;; E(G) and Y,;; E(G) with X n Y = 0_ In this paper, we study the minimum edge-connectivity of a graph G such that for any u,v E V(G) (including u = v), G has a spanning (u,v)-trail H such that X,;; E(H) and Y n E(H) = 0-1. IntroductionWe fo!low the notation of Bondy and Murty [1], except that graphshave no loops. For a graph G, a trail is a vertex-edge alternating sequence Vo, e1, v1, e2, · · · , ek-1, Vk-l, ek, Vk such that all the e/s are distinct and ei =v,_,v, for all i (1 :S: i :S: k). Let e', e" E E(G). A trail in G is ca!led an ( e' i e")-trail if its first edge is e' and its last edge is e". For u, v E V ( G), a ( u, v )-trail of G is a trail in G whose origin is u and whose terminus is v. A trail His ca!led a spanning trail if V(H) = V(G)_ If u = v, then a"'chen@butler.edu ARS COMBINATORIA 115(2014), pp. 175-186 

Edge-connectivities for spanning trails with  prescribed edges

https://digitalcommons.butler.edu/cgi/viewcontent.cgi?article=2049&amp;context=facsch_papers

Edge-connectivities for spanning trails with prescribed edges

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