✦ LIBER ✦

Cycles containing many vertices of large degree

✍ Scribed by H.J. Veldman

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 446 KB
Volume: 101
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90612-j

No coin nor oath required. For personal study only.

✦ Synopsis

Veldman, H.J., Cycles containing many vertices of large degree, Discrete Mathematics 101 (1992) 319-325. Let G be a 2-connected graph of order n, r a real number and V, = {u E V(G) ( d(v) 3 r}.

📜 SIMILAR VOLUMES

Cycles through vertices of large maximum

Cycles through vertices of large maximum degree

✍ Bill Jackson 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 442 KB

## Abstract Let __G__ be a 2‐connected graph on __n__ vertices with maximum degree __k__ where __n__ ≤ 3__k__ ‐ 2. We show that there is a cycle in __G__ that contains all vertices of degree __k.__ © 1995 John Wiley & Sons, Inc.

Cycles containing all vertices of maximu

Cycles containing all vertices of maximum degree

✍ H. J. Broersma; J. Den Van Heuvel; H. A. Jung; H. J. Veldman 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 539 KB

## Abstract For a graph __G__ and an integer __k__, denote by __V__~__k__~ the set {__v__ ∈ __V__(__G__) | __d__(__v__) ≥ __k__}. Veldman proved that if __G__ is a 2‐connected graph of order __n__ with __n__ ≤ __3k ‐ 2__ and |__V__~__k__~| ≤ __k__, then __G__ has a cycle containing all vertices of

Cycles through prescribed vertices with

Cycles through prescribed vertices with large degree sum

✍ Katsuhiro Ota 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 366 KB

Cycles through Large Degree Vertices in

Cycles through Large Degree Vertices in Digraphs: A Generalization of Meyniel's Theorem

✍ Kenneth A. Berman; Xin Liu 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 191 KB

Let D=(V, E) be a digraph with vertex set V of size n and arc set E. For u # V, let d(u) denote the degree of u. A Meyniel set M is a subset of V such that d(u)+d(v) 2n&1 for every pair of nonadjacent vertices u and v belonging to M. In this paper we show that if D is strongly connected, then every

New Constructions of Bipartite Graphs on

New Constructions of Bipartite Graphs on m, n Vertices with Many Edges and Without Small Cycles

✍ F. Lazebnik; V.A. Ustimenko; A.J. Woldar 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 293 KB

Graphic sequences have realizations cont

Graphic sequences have realizations containing bisections of large degree

✍ Stephen G. Hartke; Tyler Seacrest 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 233 KB

A __bisection__ of a graph is a balanced bipartite spanning sub‐graph. Bollobás and Scott conjectured that every graph __G__ has a bisection __H__ such that deg~__H__~(__v__) ≥ ⌊deg~__G__~(__v__)/2⌋ for all vertices __v__. We prove a degree sequence version of this conjecture: given a graphic sequen