نتایج جستجو برای: cubic graph

تعداد نتایج: 230895  

Journal: :J. Comb. Theory, Ser. B 2016
Katherine Edwards Daniel P. Sanders Paul D. Seymour Robin Thomas

A graph is apex if there is a vertex whose deletion makes the graph planar, and doublecross if it can be drawn in the plane with only two crossings, both incident with the infinite region in the natural sense. In 1966, Tutte [9] conjectured that every two-edge-connected cubic graph with no Petersen graph minor is three-edge-colourable. With Neil Robertson, two of us showed that this is true in ...

Journal: :Appl. Math. Lett. 2012
Ko-Wei Lih Daphne Der-Fen Liu

A strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they are incident to a common edge or share an endpoint. The strong chromatic index of a graph G, denoted sχ′(G), is the minimum number of colors needed for a strong edge coloring of G. A Halin graph G is a plane graph constructed from a tree T without vertice...

Journal: :Discrete Applied Mathematics 2000
Dominique Buset

We prove that there is no cubic graph with diameter 4 on 40 vertices. This implies that the maximal number of vertices of a (3,4)-graph is 38. ? 2000 Elsevier Science B.V. All rights reserved.

Journal: :Journal of Graph Theory 2008
James F. Geelen Anjie Guo David McKinnon

We prove that every simple cubic planar graph admits a planar embedding such that each edge is embedded as a straight line segment of integer length. © 2008 Wiley Periodicals, Inc. J Graph Theory 58: 270–274, 2008

Journal: :Graphs and Combinatorics 2004
Xiao-Dong Zhang Stanislaw Bylka

In this paper, we prove that a cubic line graph G on n vertices rather than the complete graph K4 has b3c vertex-disjoint triangles and the vertex independence number b3c. Moreover, the equitable chromatic number, acyclic chromatic number and bipartite density of G are 3, 3, 79 respectively.

Journal: :Australasian J. Combinatorics 1990
Sheng Bau

In this paper, obtain necessary and sufficient condition for 3-connected cubic graph to have a containing any set of nine vertices and an Vve also prove that in every 3-connected cubic planar any set of fourteen vertices and is contained in a cycle. As there is 3-connected cubic planar that of fifteen vertices and an not on any cycle, the result is the best

Journal: :Electr. J. Comb. 2011
Makoto Araya Gábor Wiener

We present a cubic planar hypohamiltonian graph on 70 vertices, improving the best known bound of 94 by Thomassen and derive some consequences concerning longest paths and cycles of planar 3-connected graphs. We also show that cubic planar hypohamiltonian graphs on n vertices exist for every even number n ≥ 86 and that cubic planar hypotraceable graphs exist on n vertices for every even number ...

2006
Manindra Agrawal Nitin Saxena

We study the isomorphism problem of two “natural” algebraic structures – F-algebras and cubic forms. We prove that the F-algebra isomorphism problem reduces in polynomial time to the cubic forms equivalence problem. This answers a question asked in [AS05]. For finite fields of the form 3 6 |(#F − 1), this result implies that the two problems are infact equivalent. This result also has the follo...

2016
Zdenek Dvorak Daniel Kral Bojan Mohar

We prove that every simple 2-connected cubic n-vertex graph contains a spanning closed walk of length at most 9n/7 − 1, and that such a walk can be found in polynomial time. This yields a polynomial-time 9/7-approximation algorithm for the graphic TSP for 2-connected cubic graphs, which improves the previously known approximation factor of 1.3 for 2-connected cubic graphs. On the negative side,...

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