𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Characterizations of n-connected and n-line connected graphs

✍ Scribed by Don R Lick


Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
147 KB
Volume
14
Category
Article
ISSN
0095-8956

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


On n-connected graphs
✍ Branko GrΓΌnbaum πŸ“‚ Article πŸ“… 1969 πŸ› John Wiley and Sons 🌐 English βš– 183 KB

The main aim of the present note is the proof of a variant of the MENGER-WHITNEY theorem on n-connected graphs (Theorem 1 below). While the result itself is well known (being, for example, a special case of the theorem of MENGER mentioned in Remark I), two of its aspects deserve attention. First, it

Fragments in kcritical n-connected graph
✍ Su Jianji πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 413 KB

## Abstract Madar conjectured that every __k__‐critical __n__‐connected non‐complete graph __G__ has (2__k__ + 2) pairwise disjoint fragments. We show that Mader's conjecture holds if the order of __G__ is greater than (__k__ + 2)__n__. From this, it implies that two other conjectures on __k__‐crit

On Minimally (n, Ξ»)-Connected Graphs
✍ Atsushi Kaneko; Katsuhiro Ota πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 128 KB

A graph G is (n, \*)-connected if it satisfies the following conditions: (1) |V(G)| n+1; (2) for any subset S V(G) and any subset L E(G) with \* |S| +|L| <n\*, G&S&L is connected. The (n, \*)-connectivity is a common extension of both the vertex-connectivity and the edge-connectivity. An (n, 1)-conn

On k-critical, n-connected graphs
✍ Stephen Maurer; Peter J. Slater πŸ“‚ Article πŸ“… 1977 πŸ› Elsevier Science 🌐 English βš– 718 KB

A graph G which iit n-connected (but not (I! I)-connected) is defined ro be k-xitical if for every S 6; V(G), where f S i d k. the connectivity of G -I S is h -/S ia We will say that G is an (n\*,k\*) graph if G is n-conneckxt (b:lt nat (n t Itconnected) and k-crirical (hut not (k c l)criticaf). Thi

Graphs with prescribed connectivity and
✍ Douglas Bauer; Ralph Tindell πŸ“‚ Article πŸ“… 1979 πŸ› John Wiley and Sons 🌐 English βš– 118 KB

## Abstract Chartrand and Stewart have shown that the line graph of an __n__‐connected graph is itself __n__‐connected. This paper shows that for every pair of integers __m__ > __n__ > 1 there is a graph of point connectivity __n__ whose line graph has point connectivity __m__. The corresponding qu

All 4-connected Line Graphs of Claw Free
✍ Matthias Kriesell πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 109 KB

Thomassen conjectured that every 4-connected line graph is hamiltonian. Here we shall see that 4-connected line graphs of claw free graphs are hamiltonian connected.