منابع مشابه
Spanning 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 کاملAOE-Trails Constructing for a Plane Connected 4-Regular Graph
The polynomial algorithm for constructing a special Eulerian cycle in a plane connected 4-regular graph G = (V,E) is presented in the paper. First of all any cycle of the passed edges does not contain any unpassed edges (the condition of ordered enclosing (OE-cycle). At second, the next edge of this cycle can be chosen from one of two neighbouring edges (left or right) of a cyclic order for the...
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 کاملSpanning 2-trails from degree sum conditions
Suppose G is a simple connected n-vertex graph. Let σ3(G) denote the minimum degree sum of three independent vertices in G (which is ∞ ifG has no set of three independent vertices). A 2-trail is a trail that uses every vertex at most twice. Spanning 2-trails generalize hamilton paths and cycles. We prove three main results. First, if σ3(G) ≥ n−1, then G has a spanning 2-trail, unless G ∼= K1,3....
متن کاملOn Spanning 2-trees in a Graph
A k-tree is either a complete graph on k vertices or a graph T that contains a vertex whose neighbourhood in T induces a complete graph on k vertices and whose removal results in a k-tree. A subgraph of a graph is a spanning k-tree if it is a k-tree and contains every vertex of the graph. This paper is concerned with spanning 2-trees in a graph. It is shown that spanning 2-trees have close conn...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8121