𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the chromatic uniquenes of bipartite graphs

✍ Scribed by Pablo M Salzberg; Miguel A López; Reinaldo E Giudici


Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
500 KB
Volume
58
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis


We prove the chromatic uniqueness of the following infinite families of bipartite graphs: Km,,,+k, l~rt3K,,,,,,,+k, with m~>2 and 0~ 3, where K~,,, denote the graph obtained from K,,,n by deleting one edge. As a particular case we prove a conjecture made by C.Y. Chao in


📜 SIMILAR VOLUMES


The chromatic uniqueness of complete bip
✍ Shaoji Xu 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 585 KB

Xu, S., The chromatic uniqueness of complete bipartite graphs, Discrete Mathematics 94 (1991) 153-159. This paper is partitioned into two parts. In the first part we determine the maximum number of induced complete bipartite subgraphs in graphs with some given conditions. Using a theorem given in th

The chromaticity of complete bipartite g
✍ C. P. Teo; K. M. Koh 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 364 KB 👁 1 views

## Abstract Let __K(p, q), p ≤ q__, denote the complete bipartite graph in which the two partite sets consist of __p__ and __q__ vertices, respectively. In this paper, we prove that (1) the graph __K(p, q)__ is chromatically unique if __p__ ≥ 2; and (2) the graph __K(p, q)__ ‐ __e__ obtained by del

A generalized construction of chromatic
✍ Michael Plantholt 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 378 KB

W e prove that any graph with maximum degree n which can be obtained by removing exactly 2n -1 edges from the join K? -K, ,, is n-critical This generalizes special constructions of critical graphs by S Fiorini and H P Yap, and suggests a possible extension of another general construction due to Yap

The total chromatic number of regular gr
✍ J.K. Dugdale; A.J.W. Hilton 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 705 KB

We show that a regular graph G of order at least 6 whose complement c is bipartite has total chromatic number d(G) + 1 if and only if (i) G is not a complete graph, and (ii) G#K when n is even. As an aid in"';he proof of this, we also show that , for n>4, if the edges of a Hamiltonian path of Kzn a

On the bipartite independence number of
✍ Odile Favaron; Pedro Mago; Oscar Ordaz 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 603 KB

Venezuela Ap. 47567, Caracas Favaron, O., P. Mago and 0. Ordaz, On the bipartite independence number of a balanced bipartite graph, Discrete Mathematics 121 (1993) 55-63. The bipartite independence number GI aIp of a bipartite graph G is the maximum order of a balanced independent set of G. Let 6 b

On the Pagenumber of Complete Bipartite
✍ Hikoe Enomoto; Tomoki Nakamigawa; Katsuhiro Ota 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 324 KB

The pagenumber p(G) of a graph G is defined as the smallest n such that G can be embedded in a book with n pages. We give an upper bound for the pagenumber of the complete bipartite graph K m, n . Among other things, we prove p(K n, n ) w2nÂ3x+1 and p(K wn 2 Â4x, n ) n&1. We also give an asymptotic