Báo cáo toán học: "Nowhere-zero 3-flows in squares of graphs" pdf
Báo cáo toán học: "Nowhere-zero 3-flows in squares of graphs" pdf
... 3-flow. In this paper, we give a complete characterization of graphs whose
squares admit nowhere-zero 3-flows and thus confirm Tutte’s 3-flow conjecture for
the family of squares of graphs.
1 Introduction
All ... is contained in a circuit
of length 3 or 4.
By contradiction. Let G
1
be the graph obtained from G by deleting the edge e and
adding a new vertex y
and a new edge xy...
Báo cáo toán học: " Long heterochromatic paths in edge-colored graphs" potx
... heterochromatic
path of length l + 1, a contradiction to the choice of P .
So, we get that i
1
/∈ C({u
1
v
s
,u
2
v
s
, ,u
l
v
s
}).
Now we turn to proving our main theorem.
4. Proof of Theorem 3.1
Proof. We ... vertex v in G with 8 ≤ k
≤ k − 1. In the following, all the notations are the same
as in Section 3. Since d
c
(v) ≥ k>k− 1 for every vertex v of G, G has a heteroch...
Báo cáo toán học: " Binary words containing infinitely many overlaps" pdf
... the beginning of w.
4 Words containing in nitely many overlaps
In this section we construct various in nite α power-free binary words containing in nitely
many overlaps. We begin by considering ... Thus, each
1 in b introduces an overlap in w
b
. Since uncountably many binary sequences contain
in nitely many 1’s, uncountably many of the w
b
are 7/3 power-free words containing
i...
Báo cáo toán học: "Geodetic topological cycles in locally finite graphs" docx
... (D
i
)
i∈I
of subsets of E thin if no edge lies in D
i
for in nitely many
indices i. Let the (thin) sum
F of this family be the set of all edges that lie in D
i
for
an odd number of indices i, ... closed, every point in P \ C
is contained in a C-arc in P. Suppose no C-arc in P is a shortcut of C. We can find a
family (W
i
)
i∈N
of countably many internally disjoint...
Báo cáo toán học: "Colorings and Nowhere-Zero Flows of Graphs in Terms of Berlekamp’s Switching Game" pptx
... duality
between proper colorings and nowhere-zero flows, the second one uses an interpretation
of a nowhere-zero point of a certain incidence matrix as a “nowhere-zero coloring” of the
underlying graph.
Part ... Orientations of Graphs. Combinatorica 12
(1992), 125–134.
[AlTa2] N. Alon, M. Tarsi: A Nowhere-zero Point in Linear Mappings. Combin atorica 9
(1989), 393–395.
the electronic...
Báo cáo toán học: "Chung-Feller Property in View of Generating Functions" pot
... contracting u and v into one point. Let P
′
denote t his new
lattice pat h and w the new point obtained by contracting u and v. Clearly, P
′
∈ L
N,S
M
and
w is one of the minimum points of P
′
, ... The combination
of P
′
and w yields a new interpretation of CF
M
(x, y) by defining
(L
N,S
M
, W) = {(P
′
, w) | P
′
∈ L
N,S
M
and w is one of the minimum points of P
′
}.
The bivariate...
Báo cáo toán học: "Fractional biclique covers and partitions of graphs" ppsx
... k,ofG
whoseedgesetscovertheedgesetofG. That is, each edge of G is in at least one of the
bicliques in B.Thebiclique cover number, bc(G), of a graph G is the minimum number
of bicliques in a biclique cover of G.Abiclique ... edges e of G.
Proof. It follows immediately from (2) and (4) that bc
∗
(G) ≤ bp
∗
(G) since a weighting v
of the edges of G that satisfies the constra...
Báo cáo toán hoc:" Some Results on Chromatic Polynomials of Hypergraphs" pdf
... {u, v} and shrink the edge e to the edge e
by identifying u, v. e
remains chromatically active in C.k.
the electronic journal of combinatorics 16 (2009), #R94 7
A λ-coloring of H is a function ... who studied a class of non-linear
uniform hypergraphs which are named sunflower hypergraphs by Tomescu in [17]. In [18]
Tomescu gave the following formula of the corresponding chrom...
Báo cáo toán học: "New results about set colorings of graphs" ppt
... connected graphs in the whole pap er. Moreover,
the cardinality of a set S will be denoted by #S.
The notion of set coloring of a graph was introduced in 2 009 by Hegde [4]. In its
original version, ... contradiction.
• A cell of type 1 is in the same row as a cell of type 4. Denote by i the row index of
these two cells of type 1 and 4. Then i + 2
n−1
is the index of a...
Báo cáo toán học: "Loose Hamilton Cycles in Random 3-Uniform Hypergraphs" doc
... (1)
Theorem 4 is proved in Janson [4] (Theorem 11) and in Molloy, Robalewska-Szalat, Robin-
son and Wormald [8].
2 Proof of Theorem 1
We begin by letting Y be a set of size 2 rm consisting of r = O(1) copies ... satisfying the
conditions of Theorem 3.
There is a minor technical point in that we can only use Theorem 2 to prove the existence
of a randomly coloured (multi-)graph...
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