D-resolvability of vertices in planar graphs
نویسندگان
چکیده
منابع مشابه
D-resolvability of vertices in planar graphs
It is well known that a vertex of degree 5 in a planar graph is not Dreducible. However, it remains an open question whether all vertices in such a graph areD-resolvable. If so, it would be a stronger result than mere 4-colorability. To investigate the question, we designed and implemented two algorithms, one to 4-color a planar graph and the other to generate internally 6-connected triangulati...
متن کاملOn 3-simplicial vertices in planar graphs
A vertex v in a graph G = (V, E) is k-simplicial if the neighborhood N(v) of v can be vertex-covered by k or fewer complete graphs. The main result of the paper states that a planar graph of order at least four has at least four 3simplicial vertices of degree at most five. This result is a strengthening of the classical corollary of Euler’s Formula that a planar graph of order at least four con...
متن کاملPlanar Hypohamiltonian Graphs on 40 Vertices
A graph is hypohamiltonian if it is not Hamiltonian, but the deletion of any single vertex gives a Hamiltonian graph. Until now, the smallest known planar hypohamiltonian graph had 42 vertices, a result due to Araya and Wiener. That result is here improved upon by 25 planar hypohamiltonian graphs of order 40, which are found through computer-aided generation of certain families of planar graphs...
متن کاملDrawing Planar Graphs with Many Collinear Vertices
Given a planar graph G, what is the maximum number of collinear vertices in a planar straight-line drawing of G? This problem resides at the core of several graph drawing problems, including universal point subsets, untangling, and column planarity. The following results are known: Every n-vertex planar graph has a planar straight-line drawing with Ω( √ n) collinear vertices; for every n, there...
متن کاملCycles Through 23 Vertices in 3-Connected Cubic Planar Graphs
We establish that if A is a set of at most 23 vertices in a 3-connected cubic planar graph G, then there is a cycle in G containing A. This result is sharp. AMS Classification: 05C38 Let G be a 3-connected cubic planar graph and let A ⊆ V (G). It was shown in [4] that if |A| ≤ 19 there is a cycle C in G such that A ⊆ V (C). In this paper we show that if |A| ≤ 23, then G contains a cycle through...
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: Journal of Graph Algorithms and Applications
سال: 2017
ISSN: 1526-1719
DOI: 10.7155/jgaa.00433