Decomposing graphs into edges and triangles 65
Decomposing graphs into edges and triangles
... contains a version with a different lower order term. We would also like to mention a closely related variant of the problem sug- gested by Erd˝os, where the cliques in the decomposition have weights one less than their ...
11
Decomposing Berge graphs
... Since F ( X2 is an output of the lemma, we may assume up to a symmetry F = X2 . If there is an outgoing path of odd length from A2 to B2, then there is by Lemma 2.4 an outgoing path P from A1 to B1 of odd length. Hence ...
50
Monochromatic triangles in three coloured graphs
... where the σ i ’s are types, L i ∈ A σ i , the M k ’s are 3-coloured complete graphs and λ k ≥ 0 for all k. Equation (4) clearly implies that K red 3 + K blue 3 + K green 3 ≥ 0.04, which is the translation of claim ...
16
On Tensor Product of Graphs, Girth and Triangles
... undirected graphs without loops or multiple ...two graphs [8] as follows: The tensor product of two graphs G 1 and G 2 is the graph, denoted by G 1 ⊕ G 2 , with vertex ...
9
Triangles in uniquely 3-colorable graphs on surfaces
... of triangles in uniquely 3-colorable graphs on ...two triangles, and by Aksionov in 1977 that if the number of vertices is at least five, then the uniquely 3-colorable planar graph contains at least ...
15
2 Outerplanar graphs without adjacent triangles
... Finally, assume that G has a cut-vertex. If G is a tree then we can color all its edges with 0. Now suppose that G is not a tree, and let us construct a 2-connected graph H from G as follows: Take an arbitrary ...
11
Decomposing degenerate graphs into locally irregular subgraphs
... 2. Decomposing good cacti into locally irregular subgraphs Throughout this paper, for a given subset F ⊆ E(G) ...k-degenerate graphs can, in general, be decomposed into a certain number of particular ...(as ...
16
Colouring of Finite Sets and Colouring of Edges of Finite Graphs
... infinite edges partition into edges classes (colour classes), in this paper we use same results inpaper [1] for finite sets partition into families of disjoint sets anduse same results results inpaper [3] ...
13
On changing behavior of edges of some special classes of graphs ii
... ( @2 ), ( @2 ), ( @2 ) and ( @ 2 ) are given fig 13, fig 14, fig 15 and fig 16 respectively. CONCLUSION In this paper, we investigated a non-Near skolem difference mean graph G and introduced a new parameter to check ...
6
Generating Chordal Graphs with few Fill-in Edges: An Experimental Study
... no induced chordless cycle on four or more vertices. Tringulation is classified into Minimal and Minimum, where both the approach seems to minimize the number of edges added. A comparison has been drawn amongst ...
76
The bipartite edge frustration of graphs under subdivided edges and their related sums
... 4 edges. Those bounds were further improved for various classes of graphs; for example, the lower bound of 4 5 | E ( G )| was established for cubic triangle-free graphs [ 4 ] and also for sub-cubic ...
7
All Pairs Shortest Paths for Graphs with Small Integer Length Edges
... the distance from v i to v k along the path which is being built and a unique index num(k) which enables us to determine which vertex comes first on the path. The refinement step is simple: we use the witnesses from the ...
12
The number of edges on generalizations of Paley graphs
... Paley graphs by counting the number of edges of the subgraph containing only those nodes x for which x and x − 1 are quadratic ...of edges of generalizations of these subgraphs using Gaussian ...
13
Asymptotic structure of graphs with the minimum number of triangles
... Many proofs in extremal graph theory proceed by considering possible densities of small subgraphs and deriving various inequalities between them. These calculations often become very cumbersome and difficult to keep track ...
25
Bounds on the eigenvalues of graphs with cut vertices or edges
... extremal graphs having the maximal Laplacian spectral radius of B n k , the set of all connected bipartite graphs with n vertices and k cut ...extremal graphs with the minimal least eigenvalue of G n ...
12
Subsets of Cayley Graphs that Induce Many Edges
... Cayley graphs on arbitrary finite Abelian groups that implies the conjecture and can be considered as a “highly asymmetric Balog–Szemerédi–Gowers theorem” when it ...
29
b-chromatic Number for the Graphs Obtained by Duplicating Edges
... the graphs E n , F n and the graphs obtained by duplicating all the edges of path, cycle, complete graph, wheel graph, Ladder graph L n by ...
13
Grid graphs with diagonal edges and the complexity of Xmas mazes
... grid graphs with diagonal edges, depending on whether one or both diagonal edges in a unit square are ...grid graphs, while the latter is L-complete (NL- complete for directed grid ...
16
Moving in temporal graphs with very sparse random availability of edges
... temporal graphs, i.e. graphs, each edge of which is assigned a set of discrete time-labels drawn from a set of ...whose edges are assigned a strictly increasing sequence of ...the edges of the ...
30
Nearest-neighbour Markov point processes on graphs with Euclidean edges
... closed edges emanating from a single ...such edges coincides with the sequential neighbourhood relation with respect to an ordering defined by the parametrisations on the ...the edges that is closest ...
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