 By Okamura H.

Read or Download 2-reducible cycles containing three consecutive edges in (2k + 1)-edge-connected graphs PDF

Best graph theory books

Fan R. K. Chung's Spectral Graph Theory PDF

This ebook relies on 10 lectures given on the CBMS workshop on spectral graph conception in June 1994 at Fresno country collage. Chung's well-written exposition will be likened to a talk with a superb instructor - one that not just delivers the proof, yet tells you what's quite happening, why it really is worthy doing, and the way it truly is relating to commonly used principles in different parts.

Hypergraph theory : an introduction by Alain Bretto PDF

This publication offers an advent to hypergraphs, its objective being to beat the inability of modern manuscripts in this concept. within the literature hypergraphs have many different names reminiscent of set structures and households of units. This paintings offers the speculation of hypergraphs in its most unique elements, whereas additionally introducing and assessing the most recent ideas on hypergraphs.

Ignacio M. Pelayo's Geodesic Convexity in Graphs PDF

​​​​​​​​Geodesic Convexity in Graphs is dedicated to the learn of the geodesic convexity on finite, basic, attached graphs. the 1st bankruptcy contains the most definitions and effects on graph idea, metric graph thought and graph course convexities. the subsequent chapters concentration completely at the geodesic convexity, together with motivation and history, particular definitions, dialogue and examples, effects, proofs, workouts and open difficulties.

Every Planar Map is Four Colorable - download pdf or read online

During this quantity, the authors current their 1972 facts of the celebrated 4 colour Theorem in a close yet self-contained exposition available to a normal mathematical viewers. An emended model of the authors' facts of the concept, the e-book comprises the whole textual content of the supplementations and checklists, which initially seemed on microfiche.

Additional resources for 2-reducible cycles containing three consecutive edges in (2k + 1)-edge-connected graphs

Example text

Paths and edge-connectivity in graphs. J. Comb. Theory Ser. B 37, 151172 (1984) 6. : Paths in k-edge-connected graphs. J. Comb. Theory Ser. B 45, 345-355 (1988) 7. : Cycles containing three consecutive edges in 2k-edge-connected graphs, Topics in Combinatorics and Graph Theory (eds. R. Bodendiek and R. Henn), PhysieaVerlag Heidelberg (1991), 549-553 8. : 2-reducible cycles containing two specified edges in (2k + 1)-edgeconnected graphs, Contemporary Math.

In (A) and (B), if x e X1 vl, then e(x, X 2 ) > ~ + 1, and so IXxl = 2 since e(v~,X2)> 2, R 2 = (x) and e(v~) = k + 1, which contradicts e(v~)= k in (A). 11). In (T), we can choose P* such that IE(P*)N O(X1)I = 1. For otherwise, starting from Ux along P*, let z be the first vertex in X1, then X 2 ÷ v~ separates z from u2. Then there are disjoint D~, D2 c_ V(G) - (X2 + vl) such that V(G) = Dx O D 2 (3 X 2 (J {01 }, e(D1, D2) --- 0, z 6 D1 and u 2 ~ D 2. 8). Thus Xx = DIUD2U{vl} = {vt,v2,z}. 6) e(z, X 2 ) < ~ and e(z, v l) < ~, a contradiction.

Ann. Discrete Math. 3, 145-164 (1978) 4. : Paths in graphs, reducing the edge-connectivity only by two. Graphs and Comb. I, 81-89 (1985) 5. : Paths and edge-connectivity in graphs. J. Comb. Theory Ser. B 37, 151172 (1984) 6. : Paths in k-edge-connected graphs. J. Comb. Theory Ser. B 45, 345-355 (1988) 7. : Cycles containing three consecutive edges in 2k-edge-connected graphs, Topics in Combinatorics and Graph Theory (eds. R. Bodendiek and R. Henn), PhysieaVerlag Heidelberg (1991), 549-553 8. : 2-reducible cycles containing two specified edges in (2k + 1)-edgeconnected graphs, Contemporary Math.