Removable edges in a cycle of a 4-connected graph
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چکیده
منابع مشابه
Removable edges in a cycle of a 4-connected graph
Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G − e; second, for all the vertices x of degree 3 in G− e, delete x from G− e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G a e. If G a...
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Let G be a 4-connected graph. For an edge e of G; we do the following operations on G: first, delete the edge e from G; resulting the graph G e; second, for all the vertices x of degree 3 in G e; delete x from G e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G~e: If G~e is st...
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An edge e of a k-connected graph G is said to be a removable edge if G a e is still k-connected, where Ga e denotes the graph obtained from G by deleting e to get G− e and, for any end vertex of e with degree k− 1 in G− e, say x, deleting x and then adding edges between any pair of non-adjacent vertices in NG−e(x). Xu and Guo [28] proved that a 5-connected graph G has no removable edge if and o...
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Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G e; second, for all vertices x of degree 3 in G e, delete x from G e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G e. If G e is 4-conn...
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All rights reserved. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical , photocopying, recording, or otherwise, without prior permission from the copyright owner. Dit proefschrift is goedgekeurd door de promotoren Preface It took almost four years to complete this dissertation which is about the theory on rem...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.05.015