On vertex-degree restricted subgraphs in polyhedral graphs
نویسندگان
چکیده
منابع مشابه
Computing and Sampling Restricted Vertex Degree Subgraphs and Hamiltonian Cycles
Let G = (V, E) be a bipartite graph embedded in a plane (or n-holed torus). Two subgraphs of G differ by a Z-transformation if their symmetric difference consists of the boundary edges of a single face—and if each subgraph contains an alternating set of the edges of that face. For a given φ : V 7→ Z, Sφ is the set of subgraphs of G in which each v ∈ V has degree φ(v). Two elements of Sφ are sai...
متن کاملVertex-disjoint subgraphs with high degree sums
For a graph G, we denote by σ2(G) the minimum degree sum of two non-adjacent vertices if G is non-complete; otherwise, σ2(G) = +∞. In this paper, we give the following two results; (i) If s1 and s2 are integers with s1, s2 ≥ 2 and if G is a non-complete graph with σ2(G) ≥ 2(s1 + s2 + 1) − 1, then G contains two vertexdisjoint subgraphs H1 and H2 such that each Hi is a graph of order at least si...
متن کاملConnected Tropical Subgraphs in Vertex-Colored Graphs
A subgraph of a vertex-colored graph is said to be tropical whenever it contains each color of the graph. In this work we study the problem of finding a minimal connected tropical subgraph. We first show that this problem is NP-Hard for trees, interval graphs and split graphs, but polynomial when the number of colors is logarithmic in terms of the order of the graph (i.e. FPT). We then provide ...
متن کاملRestricted vertex multicut on permutation graphs
Given an undirected graph and pairs of terminals theRestricted Vertex Multicut problem asks for a minimum set of nonterminal vertices whose removal disconnects each pair of terminals. The problem is known to be NP-complete for trees and polynomial-time solvable for interval graphs. In this paper we give a polynomial-time algorithm for the problem on permutation graphs. Furthermore we show that ...
متن کاملSplice Graphs and their Vertex-Degree-Based Invariants
Let G_1 and G_2 be simple connected graphs with disjoint vertex sets V(G_1) and V(G_2), respectively. For given vertices a_1in V(G_1) and a_2in V(G_2), a splice of G_1 and G_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the union of G_1 and G_2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.
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: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00368-5