منابع مشابه
Spanning trails containing given edges
A graph G is Eulerian-connected if for any u and v in V (G), G has a spanning (u. v)-trail. A graph G is edge-Eulerian-connected if for any e' and elf in E(G), G has a spanning (e', elf)-trail. For an integer r ~ 0, a graph is called r-Eulerian-connected if for any X s::: E(G) with IXI ~r, and for any u, v E V(G), G has a spanning (u, v)-trail T such that X s::: E(T). The r-edge-Eulerian conne...
متن کاملSpanning Trails Connecting Given Edges
Suppose that F is the set of connected graphs such that a graph G 2 F if and only if G satisfies both (F1) if X is an edge cut of G with jX j 3, then there exists a vertex v of degree jX j such that X consists of all the edges incident with v in G, and (F2) for every v of degree 3, v lies in a k-cycle of G, where 2 k 3. In this paper, we show that if G 2 F and j0ðGÞ 3, then for every pair of ed...
متن کاملEulerian subgraphs containing given edges
For an integer l¿0, de ne SE(l) to be the family of graphs such that G ∈SE(l) if and only if for any edge subset X ⊆E(G) with |X |6l, G has a spanning eulerian subgraph H with X ⊆E(H). The graphs in SE(0) are known as supereulerian graphs. Let f(l) be the minimum value of k such that every k-edge-connected graph is in SE(l). Jaeger and Catlin independently proved f(0) = 4. We shall determine f(...
متن کاملSpanning trails
A graph is called 2K2-free if it does not contain two independent edges as an induced subgraph. Mou and Pasechnik conjectured that every 3 2 -tough 2K2-free graph with at least three vertices has a spanning trail with maximum degree at most 4. In this paper, we confirm this conjecture. We also provide examples for all t < 54 of t-tough graphs that do not have a spanning trail with maximum degre...
متن کاملGraphs without spanning closed trails
Jaeger [J. Graph Theory 3 (1979) 91-93] proved that if a graph has two edge-disjoint spanning trees, then it is supereulerian, i.e., that it has a spanning closed trail. Catlin [J. Graph Theory 12 (1988) 29-45] showed that if G is one edge short of having two edge-disjoint spanning trees, then G has a cut edge or G is supereulerian. Catlin conjectured that if a connected graph G is at most two ...
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: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.10.022