𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Mader’s Conjecture On Extremely Critical Graphs

✍ Scribed by Matthias Kriesell

Publisher
Springer-Verlag
Year
2006
Tongue
English
Weight
477 KB
Volume
26
Category
Article
ISSN
0209-9683

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Proof of Mader's conjecture on k-critica
Proof of Mader's conjecture on k-critical n-connected graphs
✍ Su Jianji 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 201 KB 👁 1 views

## Abstract Mader conjectured that every __k__‐critical __n__‐connected noncomplete graph __G__ has __2k__ + 2 pairwise disjoint fragments. The author in 9 proved that the conjecture holds if the order of __G__ is greater than (__k__ + 2)__n__. Now we settle this conjecture completely. © 2004 Wiley

On the critical graph conjecture
On the critical graph conjecture
✍ Hian Poh Yap 📂 Article 📅 1980 🏛 John Wiley and Sons 🌐 English ⚖ 222 KB

## Abstract Gol'dberg has recently constructed an infinite family of 3‐critical graphs of even order. We now prove that if there exists a __p__(≥4)‐critical graph __K__ of odd order such that __K__ has a vertex __u__ of valency 2 and another vertex __v__ ≠ __u__ of valency ≤(__p__ + 2)/2, then ther

Remarks on the critical graph conjecture
Remarks on the critical graph conjecture
✍ I. Broere; C.M. Mynhardt 📂 Article 📅 1979 🏛 Elsevier Science 🌐 English ⚖ 344 KB

The vertex-critical graph conjecture (critical graph conjecture respectively) states that every vertex-critical (critical) graph has an odd number of vertices. In this note we prove that if G is a critical graph of even order, then G has at least three vertices of less-than-maximum valency. In addit

On Ádám's conjecture for circulant graph
On Ádám's conjecture for circulant graphs
✍ Mikhail Muzychuk 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 643 KB

Adfim's (1967) conjecture formulates necessary and sufficient conditions for cyclic (circulant) graphs to be isomorphic. It is known that the conjecture fails if n is divisible by either 8 or by an odd square. On the other hand, it was shown in [?] that the conjecture is true for circulant graphs w