Large Isaacs' graphs are maximally non- Hamilton-connected
نویسندگان
چکیده
منابع مشابه
Maximally Connected Graphs and Digraphs
Preface Graphs are often used as a model for networks, for example transport networks, telecommunication systems, a network of servers and so on. Typically, the networks and thus the representing graphs are connected; that means, that there exists a path between all pairs of two vertices in the graph. But sometimes an element of the network fails, for the graphs that means the removal of a vert...
متن کاملHamilton-connected indices of graphs
Let G be an undirected graph that is neither a path nor a cycle. Clark and Wormald [L.H. Clark, N.C. Wormald, Hamiltonian-like indices of graphs, ARS Combinatoria 15 (1983) 131–148] defined hc(G) to be the least integerm such that the iterated line graph Lm(G) is Hamilton-connected. Let diam(G) be the diameter of G and k be the length of a longest path whose internal vertices, if any, have degr...
متن کاملmaximally edge - connected and super - edge - connected graphs ∗
Let G be a connected graph with minimum degree δ and edgeconnectivity λ. A graph is maximally edge-connected if λ = δ, and it is superedge-connected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. In this paper, we show that a connected graph or a connected triangle-free graph is maximally edge-connected or sup...
متن کاملOn 1-Hamilton-connected claw-free graphs
A graph G is k-Hamilton-connected (k-hamiltonian) if G−X is Hamilton-connected (hamiltonian) for every setX ⊂ V (G) with |X| = k. In the paper, we prove that (i) every 5-connected claw-free graph with minimum degree at least 6 is 1Hamilton-connected, (ii) every 4-connected claw-free hourglass-free graph is 1-Hamilton-connected. As a byproduct, we also show that every 5-connected line graph with...
متن کاملHamilton Connected Derangement Graphs on Sn
We consider the derangements graph in which the vertices are permutations of f ng Two vertices are joined by an edge if the corresponding permuta tions di er in every position The derangements graph is known to be hamil tonian and it follows from a recent result of Jung that every pair of vertices is joined by a Hamilton path We use this result to settle an open question by showing that it is p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90049-n