Hamiltonian cycles and dominating cycles passing through a linear forest
نویسندگان
چکیده
منابع مشابه
Hamiltonian cycles through a linear forest
Let G be a graph of order n. A graph is linear forest if every component is a path. Let S be a set of m edges of G that induces a linear forest. An edge xy ∈ E(G) is called an S-edge if xy ∈ S. An S-edge-length of a cycle in G is defined as the number of S-edges that it contains. We prove that if the degree sum in G of every pair of nonadjacent vertices of G is at least n + m, then G contains h...
متن کاملIndependent dominating sets and hamiltonian cycles
A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r-regular uniquely hamiltonian graphs when r > 22. This improves upon earlier results of Thomassen.
متن کاملHamiltonian Cycles in Linear-Convex Supergrid Graphs
A supergrid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional supergrid. The supergrid graphs contain grid graphs and triangular grid graphs as subgraphs. The Hamiltonian cycle problem for grid and triangular grid graphs was known to be NP-complete. In the past, we have shown that the Hamiltonian cycle problem for supergrid graphs is also NP-complete. ...
متن کاملCharacterization of signed paths and cycles admitting minus dominating function
If G = (V, E, σ) is a finite signed graph, a function f : V → {−1, 0, 1} is a minusdominating function (MDF) of G if f(u) +summation over all vertices v∈N(u) of σ(uv)f(v) ≥ 1 for all u ∈ V . In this paper we characterize signed paths and cycles admitting an MDF.
متن کاملCovering a bipartite graph with cycles passing through given edges
We propose a conjecture: for each integer k 2:: 2, there exists N (k) such that if G = (Vb \12; E) is a bipartite graph with IV11 = 1\121 = n 2: N(k) and d( x) + d(y) 2: n + k for each pair of non-adjacent vertices x and y of G with x E V1 and y E \12, then for any k independent edges el, ... , ek of G, there exist k vertex-disjoint cycles G1, ... , Gk in G such that ei E E(Gi ) for all i E {I,...
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: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.02.031