An immersion of a square in 4-edge-connected graphs
نویسندگان
چکیده
منابع مشابه
Immersion in four-edge-connected graphs
Fix g > 1. Every graph of large enough tree-width contains a g × g grid as a minor; but here we prove that every four-edge-connected graph of large enough tree-width contains a g × g grid as an immersion (and hence contains any fixed graph with maximum degree at most four as an immersion). This result has a number of applications.
متن کاملEdge-disjoint Odd Cycles in 4-edge-connected Graphs
Finding edge-disjoint odd cycles is one of the most important problems in graph theory, graph algorithm and combinatorial optimization. In fact, it is closely related to the well-known max-cut problem. One of the difficulties of this problem is that the Erdős-Pósa property does not hold for odd cycles in general. Motivated by this fact, we prove that for any positive integer k, there exists an ...
متن کاملSpanning trails in essentially 4-edge-connected graphs
A connected graphG is essentially 4-edge-connected if for any edge cut X ofGwith |X | < 4, either G − X is connected or at most one component of G − X has edges. In this paper, we introduce a reductionmethod and investigate the existence of spanning trails in essentially 4-edge-connected graphs. As an application, we prove that if G is 4-edge-connected, then for any edge subset X0 ⊆ E(G) with |...
متن کاملZ3-connectivity of 4-edge-connected 2-triangular graphs
A graph G is k-triangular if each edge of G is in at least k triangles. It is conjectured that every 4-edge-connected 1-triangular graph admits a nowhere-zero Z3-flow. However, it has been proved that not all such graphs are Z3-connected. In this paper, we show that every 4-edge-connected 2-triangular graph is Z3-connected. The result is best possible. This result provides evidence to support t...
متن کامل2-edge-Hamiltonian-connectedness of 4-connected plane graphs
A graph G is called 2-edge-Hamiltonian-connected if for any X ⊂ {x1x2 : x1, x2 ∈ V (G)} with 1 ≤ |X| ≤ 2, G ∪ X has a Hamiltonian cycle containing all edges in X, where G ∪ X is the graph obtained from G by adding all edges in X. In this paper, we show that every 4-connected plane graph is 2edge-Hamiltonian-connected. This result is best possible in many senses and an extension of several known...
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: Progress in Informatics
سال: 2012
ISSN: 1349-8614,1349-8606
DOI: 10.2201/niipi.2012.9.7