Báo cáo toán học: "Total 4-choosability of series-parallel graphs" pptx
Báo cáo toán học: "Perfect factorisations of bipartite graphs and Latin squares without proper subrectangles" pptx
... Subsquares of N
2
squares of order 9.
In particular we note that there are 1589 main classes of N
∞
squares of order 9, yet
only 37 of these contain pan-Hamiltonian squares. In terms of reduced ... have a generalisation of Lemma 4.
§6. Small orders
For n ∈{2, 3, 5} thecatalogueofLatinsquaresin[5]showsthatthereisasinglemain
class of N
∞
square of order n,namelythatofC
n
. Acc...
Báo cáo toán học: "Competitive Colorings of Oriented Graphs" docx
... member of the second coordinate of the label of y, delete the edge x
j
y.If
the digit of z is 3 and y is not a member of the second coordinate of the label of z, delete
the electronic journal of ... Subclaims, the proof of our lemma is complete.
5 Proof of the Main Theorem
In this section, we present the proof of the main theorem. Let C be a topologically closed
class o...
Báo cáo toán học: "The Rank of a Cograph" pptx
... class of cographs.
3 Spectrum of a cograph
The characteristic polynomial ϕ(X) of the graph X is the characteristic polynomial of its
adjacency matrix A(X). The spectrum of X is the collection of ... of eigenvalues of A(X), or
equivalently, the collection of zeros of ϕ(X). The rank of X is the number of non-zero
values occurring in the spectrum.
In order to study the sp...
Báo cáo toán học: "A partition of connected graphs Gus Wiseman" pps
... ordering of the vertices
to an ordering of the edges lexicographically. A broken circuit of H ⊆ G is a set of edges
B ⊆ H such that there is some edge e ∈ G, smaller than every edge of B, such ... consists of all edges of G
with both ends in S.
We will use the symbols π and σ to denote set partitions. The notation π S means
π is a set partition of the set S. The length (numb...
Báo cáo toán học: "One-Factorizations of Regular Graphs of Order 12" pot
... one-factorization of type 4 + 4 + 4 is only possible for three graphs of order
12: the disjoint union of three copies of C
4
, the disjoint union of three copies of K
4
,and
the union of K
4
and the ... properties of the
classified one-factorizations are also tabulated.
1 Introduction
An r-factor of a graph G is an r-regular spanning subgraph of G.Anr-factorization
of G i...
Báo cáo toán học: "On Lengths of Rainbow Cycles" pptx
... yields the result that the absence of rainbow 5-cycles implies the
absence of rainbow 9-cycles.
Proof. The proof of this lemma has the same basic structure as that of Lemma 8, but
the cycles we consider ... color of this chord. On the one hand, it must agree with one
of the other edges of the n-cycle to avoid a rainbow n-cycle; on the other hand, it must
similarly agree with one...
Báo cáo toán học: "Irregularity strength of regular graphs" potx
... δ) denote the set of neighbours and the degree of
v in G, the set of vertices, the set of edges and the minimum degree of G, respectively.
By G[D] we mean an induced subgraph of G with the vertex ... V
2
, . . . , V
k
} of disjoint subsets of a set V is called a partition of V if the union of
all elements of V is V and V
i
= ∅ for every i. We shall denote as P
k
a path...
Báo cáo toán học: "Skew Spectra of Oriented Graphs" potx
... University Press, 1987.
the electronic journal of combinatorics 16 (2009), #N32 6
Skew Spectra of Oriented Graphs
Bryan Shader
Department of Mathematics
University of Wyoming, Laramie, WY 82071-3036, USA
email: ... underlying graph of G
σ
, and we denote by Sp(G) the adjacency spectrum
of G. S kew-adjacency matrix S(G
σ
) of G
σ
is intro duced, and its spectrum Sp
S
(G
σ
)
is ca...
Báo cáo toán học: "Another characterisation of planar graphs" ppt
... and at least one of them contains an
end of an edge of A
i
∩ B
since at least one of G[X
i
∩ Y ] and G[X
i
∩ Y ] contains an end
of an edge of A
i
∩ B.
the electronic journal of combinatorics ... G
∗
is
necessarily connected. Each bond of G is a circuit of G
∗
, and each circuit of G is a bond
of G
∗
. If a theorem holds for a given set T of edges of G, then the...
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