Báo cáo toán học: "One-Factorizations of Regular Graphs of Order 12" pot

... antipodal distance- regular graphs, and some distance -regular graphs with diameter d =3. The main result in this paper is a characterization of these graphs (among regular graphs with d distinct ... regular. The only known examples of these graphs are the strongly regular graphs (with diameter d = 2), the antipodal distance -regular graphs, and the distance -regular...

Ngày tải lên: 07/08/2014, 06:20

... generates many non-isomorphic graphs. We then show that most of the graphs generated have the n-e.c. property in Section 4, thereby completing the proof of Theorem 1.1. The proof of the n-e.c. property ... the graphs of Construction 2. The number of graphs without any bad pairs U, W is therefore at least 2 ( q+1 2 ) (q!) q+1  1 − c 1 exp  −c 2 q 1/2  . Theorem 1.1 results...

Ngày tải lên: 07/08/2014, 06:23

... α α α γ γ γ γ γ β β β β Figure 1: The colouring of H used in the second case of the proof of Lemma 1 when n ≡ 1 (mod 3) 3.2 Proof of Lemma 1 Fix d ≥ 5, n ≥ 6, and let G be a (d − 2) -regular multigraph on the vertex ... aid of contiguity. Section 2 contains background on contiguity of random regular graphs. The main proof is presented in Section 3, while two crucial probabilis...

Ngày tải lên: 07/08/2014, 13:21

... each pair of non- adjacent neighbours has 4 common neighbours. In [3] an incomplete enumeration of strongly regular (40, 12, 2, 4) graphs established the existence of at least 27, all of which have ... electronic journal of combinatorics 7 (2000), #R22 2 1 Introduction A strongly regular (40, 12, 2, 4) graph is a regular graph on 40 vertices of degree 12 such that each pai...

Ngày tải lên: 07/08/2014, 06:20

... way to describe the structure of these graphs is in terms of graph homomorphisms. One infinite sequence of cores of dense maximal triangle-free graphs was known. All graphs in this sequence are ... with chromatic number 4 of order p =3k+, −1 ≤  ≤ 1, which is the core of a triangle-free (9k−25+) -regular graph on n =27k−76 + 3 vertices. Proof. We claim that the Vega gr...

Ngày tải lên: 07/08/2014, 06:22

... given of an infinite family of n-vertex cubic graphs of girth at least 5 that have no connected dominating set of size less than 4n/7 − O(1). As we consider regular graphs that are generated u.a.r. ... use for generating cubic graphs u.a.r. and describe the notion of analysing the performance of algorithms on random graphs using systems of differential equations. Details...

Ngày tải lên: 07/08/2014, 06:23

... 2. y u <y v . Repeating the proof of Case 1 with roles of A and B switched yields this case. The proof of Claim 3.2 is the same (with C in place of B). ProofofClaim3.3.Let A ∗ =2A, B ∗ = A ∗ − ... and Weißenfels [6] considered colorings of graphs in the class U of intersection graphs of unit disks in the plane. They proved that finding chromatic number of graphs in U i...

Ngày tải lên: 07/08/2014, 08:20

... all of these graphs can be obtained from [12]. Of these 78 graphs, 24 graphs contain a clique of size 5. There are 54 graphs which do not contain a clique of size 5 but do have a clique of size ... graph has 12 vertices and is regular of degree 3. There exist (up to isomorphism) 94 regular graphs of order 12 and degree 3 (they can easily be generated using geng [8...

Ngày tải lên: 07/08/2014, 13:21

... simplification of G and let F be a flat face of G  . We know that it is a subdivision of C 2 , and each edge of F belongs to one of the two sides of C 2 . Lemma 8. Let e be an edge of G  and let ... face of G and v 1 ,v  1 ,v 2 ,v  2 vertices of F appearing along F in this order. Then G does not have two disjoint v 1 ,v 2 and v  1 ,v  2 paths. Proof. Thisisasimpleprope...

Ngày tải lên: 07/08/2014, 13:21

... some properties of this graph. Finally, Section 4 is dedicated to the proof of Theorem 2. 2 Definitions and notation In the rest of the paper, oriented graphs will be simply called graphs. ForagraphG and ... sink) of degree k will be called a k-source (resp. a k-sink). We denote by N + G (v), N − G (v)andN G (v) respectively the set of successors of v,the set of predecessors...

Ngày tải lên: 07/08/2014, 13:21