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Cycles through vertices of large maximum degree

✍ Scribed by Bill Jackson

Publisher: John Wiley and Sons
Year: 1995
Tongue: English
Weight: 442 KB
Volume: 19
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190190204

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✦ Synopsis

Abstract

📜 SIMILAR VOLUMES

Cycles through prescribed vertices with

Cycles through prescribed vertices with large degree sum

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

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 containing many vertices of large

Cycles containing many vertices of large degree

✍ H.J. Veldman 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 446 KB

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}.

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

Class 1 conditions depending on the mini

Class 1 conditions depending on the minimum degree and the number of vertices of maximum degree

✍ Thomas Niessen; Lutz Volkmann 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 694 KB

## Abstract A graph is called Class 1 if the chromatic index equals the maximum degree. We prove sufficient conditions for simple graphs to be Class 1. Using these conditions we improve results on some edge‐coloring theorems of Chetwynd and Hilton. We also improve a theorem concerning the 1‐factori

Total colorings of planar graphs with la

Total colorings of planar graphs with large maximum degree

✍ Borodin, O. V.; Kostochka, A. V.; Woodall, D. R. 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 97 KB 👁 3 views

It is proved that a planar graph with maximum degree ∆ ≥ 11 has total (vertex-edge) chromatic number ∆ + 1.