We conjecture that NDER (sin x) = cos x. The graphs
On the KŁR conjecture in random graphs
... about graphs to subgraphs of the random graph G n,p , including Ramsey’s theorem [67] and the Erd˝os-Simonovits stability theorem ...paper, we shall state and prove such a “counting version” of the K LR ...
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Erdös Conjecture on Connected Residual Graphs
... extremal graphs are specified expected for n=3, and in this paper, we prove that the minimum order of the connected 3-Kn-residual graph is found and all the extremal graphs are specified expected for ...
6
The Erdős–Hajnal conjecture for bull-free graphs
... A graphs is called bull-free if no induced subgraph of it is a ...paper we prove that every bull-free graph on n vertices contains either a clique or a stable set of size n 1 4 , thus settling the ...
10
On a conjecture of Murty and Simon on diameter 2-critical graphs
... that Conjecture 2 holds for 3 t -critical graphs of diameter three, we need strict inequality in the Hanson–Wang ...the conjecture in this case. We emphasize that without strict ...
7
The bondage number of graphs on topological surfaces and Teschner's conjecture
... connected graphs because the bondage number of a disconnected graph G is the minimum of the bondage numbers of its ...paper, we provide constant upper bounds for the bondage number of graphs on ...
19
The Merino–Welsh conjecture holds for series–parallel graphs
... (connected) graphs with few edges tend to be “tree-like” and have more acyclic orientations than spanning trees, whereas for graphs with many edges, the number of totally cyclic orientations tends to ...
18
Minimum degree conditions for the Overfull Conjecture for odd order graphs
... Overfull Conjecture states that a graph G with 3∆(G) ≥ n(G) is Class 2 if and only if it has a ∆(G)-overfull ...Overfull Conjecture is true for graphs with even order and high minimum ...paper ...
9
The validity of Tutte’s 3-flow conjecture for some Cayley graphs ∗
... [2], we deduce that every Cayley graph of valency at least 4 has a ...Cayley graphs. Since 4-regular graphs admit a nowhere- zero 2-flow, the important question about flows on Cayley graphs of ...
11
On a conjecture of Murty and Simon on diameter two critical graphs II
... extremal graphs are complete bipartite graphs with equal size partite ...sets. We use an important association with total domination to prove the conjecture for the graphs whose ...
9
Independence polynomials of well-covered graphs: Generic counterexamples for the unimodality conjecture
... (see [16]). For instance, the trees presented in Fig. 1 are well-covered as follows: T 2 is a well-covered spider, while T 1 is an edge-join of two well-covered spiders, namely, K 1 ∗ ,2 and K 1 ∗ ,1 . In [3] it was ...
9
On the Erd˝os-S´os Conjecture for graphs on n = k + 4 vertices ∗
... Erd˝os-S´os Conjecture, tree, maximum ...The graphs considered in this paper are finite, undirected, and simple (no loops or multiple ...adjacent, we say that u hits v or v hits u. If u and v are not ...
13
A proof of a conjecture on diameter 2-critical graphs whose complements are claw-free
... that Conjecture 2 holds for 3 t -critical graphs of diameter 3, we need strict inequality in the Hanson–Wang ...the conjecture in this case. We emphasize that without strict inequality ...
7
Partial product of graphs and Vizing’s conjecture
... article we obtain Vizing-like results for the domination number and the independence domination number of the partial Cartesian product of ...Moreover we study the domination number of the restricted ...
7
A Class of Graphs Approaching Vizing's Conjecture
... For any graph G = (V, E), a subset S ⊆ V dominates G if all vertices are contained in the closed neighborhood of S, that is N [S] = V . The minimum cardinality over all such S is called the domination number, written γ ...
8
Erdős-Hajnal Conjecture for Graphs with Bounded VC-Dimension
... such graphs contain independent sets of size cn s−1 1 (log n) s−2 s−1 ...-free graphs on n vertices and with no independent set of size c ′ n s+1 2 log ...4, we give a simple proof, extending ...
19
A proof of Mader's conjecture on large clique subdivisions in C4 free graphs
... section, we prove Lemma ...condition, we either find the subdivision we seek or we may assume an additional maximum degree ...then we can delete these vertices and obtain a subgraph of G ...
26
Beyond Ohba’s conjecture : a bound on the choice number of k chromatic graphs with n vertices
... noted, we may assume that G is a complete k-partite graph. We prove that in a minimal counterexample, all parts have size at most 4 and no color appears in more than two lists on one ...part. We then ...
15
Domination Game: A proof of the 3/5-Conjecture for Graphs with Minimum Degree at Least Two
... ∈ X and uv ∈ ...(G; X ∪ Y ) ≤ and γ g (G; X ∪ Y ) ≤ ...move x in the secondary game. If x ∈ Y , or if x ∈ Y but x lies on no volatile edge, then Dominator plays ...
18
Beyond Ohba s Conjecture: A bound on the choice number of k-chromatic graphs with n vertices
... noted, we may assume that G is a complete k-partite graph. We prove that in a minimal counterexample, all parts have size at most 4 and no color appears in more than two lists on one ...part. We then ...
14
f x a 0 n 1 a 0 a 1 cos x a 2 cos 2x a 3 cos 3x b 1 sin x b 2 sin 2x b 3 sin 3x a n cos nx b n sin nx n 1 f x dx y
... If we apply the Fourier Convergence Theorem to the square-wave function in Example 1, we get what we guessed from the graphs. Observe that and and similarly for the other points at which is ...
10