2024 K-minimal 3-connected cubic graphs

K-minimal 3-connected cubic graphs

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August undefined, 2024

Weball vertices of a k-connected graph have degree at least k. In 1967 minimal biconnected graphs were considered in the papers [1] and [2]. It can be deduced from the results of … WebIn the paper Li and Wu [11], the strict upper bound on xi(d)(Gamma) among the k-connected graphs Gamma with an integer k even were given, and proposed an open question: the corresponding problem on k-connected graphs with k odd. In this paper, first, we divide cubic transitive graphs into two cases: super-connectedness and non-super ...

Full article: The k-conversion number of regular graphs - Taylor

Webwhich do not have an induced copy of the claw K(1,3): Proposition 3 [6] If G is a noncomplete K(1,3)-free graph G then τ(G) = κ(G)/2. For r ≥ 4 an r-regular r-connected K(1,3)-free graph with large order need not have order a multiple of r. (For example, the line graph of a random (3,4)-biregular graph is 5-regular and almost surely 5 ... WebSince the Minimal_12_Set algorithm prefers the nodes with the highest degree, we tested the Minimal_12_Set algorithm and random algorithm on random cubic graphs, that is graphs in which each node is of degree 3. We supposed that these graphs should eliminate the advantage of adding nodes with high degrees to the minimal (1, 2)-dominating set ... drawing things to do when bored

Cycle lengths modulo k in large 3-connected cubic graphs

Webcontain a cyclic n-cut where n WebWe say that a graph is almost k-Halin if it is obtained from a simple cubic 3connected kHalin graph, which is not (k − 1)Halin and has a connected core, by deleting a vertex of its outer … WebAug 21, 2024 · A theorem of Mader, proved (in German) in this paper, says that in any edge-minimal, k -edge-connected graph on n ≥ 3 k − 2 vertices, there are at most k ( n − k) … drawing this argument further

Minimal k-Connected Non-Hamiltonian Graphs

Cubic graph - Wikipedia, the free encyclopedia - École Polytechnique

WebOct 20, 2024 · In 1996, Reed proved that the domination number (G) of every n-vertex graph G with minimum degree at least 3 is at most 3n/8. Also, he conjectured that (H) n/3 for every connected 3-regular (cubic) … Expand. 26. PDF. View 1 excerpt, references background; Save. Alert. Quasi-claw-free graphs. A. Ainouche; Mathematics. Discret. Math. WebA 3-connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected graphs based on the results in (Dawes, JCTB 40, 159-168, 1986) using two operations: adding an edge between non-adjacent vertices and splitting a vertex. To test sets of vertices and edges … drawing things togetherWebThe first interesting case is therefore 3-regular graphs, which are called cubic graphs (Harary 1994, pp. 14-15). Most commonly, "cubic graphs" is used to mean "connected cubic graphs." Note that - arc-transitive graphs … empowered employee benefits

"WebWe prove that for every d ≥ 3 there is an infinite family of Hamiltonian 3-connected graphs with minimum degree d, with a bounded number of Hamiltonian cycles. It is shown that if a 3-regular graph G has a unique longest cycle C, at least two components of G − E ( C) have an odd number of vertices on C, and that there exist 3-regular graphs ... " - K-minimal 3-connected cubic graphs

K-minimal 3-connected cubic graphs

Regular Graphs with Few Longest Cycles SIAM Journal on …

WebApr 30, 2015 · The resulting graph H_1 is 3-connected. For k\ge 2, H_k has connectivity 2. Always H_k has 14k vertices and is cubic. Fig. 1 The graph F Full size image Theorem 2.2 i (H_k)=5k and \gamma (H_k)=4k. Proof First, we prove \gamma (H_k)=4k. Since \ {a^1, b^3, b^4, a^6\} is a dominating set in F, we have \gamma (H_k) \le 4k. WebOct 19, 1996 · It is shown that the vertex cover problem (or the maximum independent set problem) remains NP-complete even for a cubic, planar, and 3-connected graph of girth greater than 3. The result...

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WebBarnette's conjecture states that every cubic bipartite polyhedral graph is Hamiltonian. By Steinitz's theorem, a planar graph represents the edges and vertices of a convex polyhedron if and only if it is polyhedral. A three-dimensional polyhedron has a cubic graph if and only if it is a simple polyhedron . And, a planar graph is bipartite if ... Web[7] R. Uehara, NP-complete problems on a 3-connected cubic planar graph and their applications, Tech. Rep. TWCU-M-0004, Tokyo Woman's Christian University (1996). [8] M. de Berg, A. Khosravi, Optimal binary space partitions in the plane, in: Proceedings of the 16th International Conference on Computing and Combinatorics, 2010, pp. 329-343.

WebProperties. As a Möbius ladder, the Wagner graph is nonplanar but has crossing number one, making it an apex graph.It can be embedded without crossings on a torus or projective plane, so it is also a toroidal graph.It has girth 4, diameter 2, radius 2, chromatic number 3, chromatic index 3 and is both 3-vertex-connected and 3-edge-connected. The Wagner … WebDec 22, 2024 · A $3$-connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected …

WebSep 2, 2024 · Abstract For any positive integer $k$, define $f (k)$ (respectively, $f_3 (k)$) to be the minimal integer $\ge k$ such that every 3-connected planar graph $G$ … WebIn mathematics, the minimum k-cut is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph to at least k connected …

WebMay 12, 2024 · We obtain the bound for k = 2 by checking all examples (there are three cubic graphs having a 2-conversion set of size 2: K4 and the two cubic graphs of order 6). For k …

WebJul 24, 2024 · The smallest 3-connected cubic graph containing H'' can be obtained from H'' by adding three edges joining the vertices of degree 2. However, there are many ways how to construct 3-connected cubic graphs containing H'' as a subgraph. For example, let G be any 3-connected cubic graph containing an induced 6-cycle C. empowered engineeringWebLemma 2.2. A minimal non-hamiltonian 3-connected bipartite cubic graph is cyclically 4-connected. Proof. Suppose that a non-hamiltonian 3-connected bipartite cubic graph G … empowered en francaisWebOct 19, 1996 · It is shown that the vertex cover problem (or the maximum independent set problem) remains NP-complete even for a cubic, planar, and 3-connected graph of girth … empowered entertainmentWebMay 22, 2014 · In this paper, we propose a related problem as follows: Given a graph G = ( V, E) and a vertex-weight function w, the goal is to find a minimum weight vertex set F ⊆ V such that every connected subgraph on k vertices has at least one vertex from F. Call such a set F as a connected k-subgraph cover ( VCC k) and the problem as a minimum weight ... empowered energy solutionsWebFeb 3, 2024 · The current paper contributes to this long line of research by proving that for every integer m and a positive odd integer k, every sufficiently large 3 -connected cubic … empowered employmentWebApr 1, 1986 · We are now prepared to show that the minimally 3-connected graphs, with the exception of K4, are precisely the graphs obtained by applying Operations 1, 2, and 3 to … drawing things to printWebLemma 2.2. A minimal non-hamiltonian 3-connected bipartite cubic graph is cyclically 4-connected. Proof. Suppose that a non-hamiltonian 3-connected bipartite cubic graph G has an inde-pendent 3-edge cut fe 1;e 2;e 3g. Divide G … empowered energy solutions san diego