Báo cáo toán học: "Partitioning 3-colored complete graphs into three monochromatic cycles" ppsx
Báo cáo toán học: "Partitioning 3-colored complete graphs into three monochromatic cycles" ppsx
... of A
3
the electronic journal of combinatorics 18 (2011), #P53 6
Partitioning 3-colored complete graphs into
three monochromatic cycles
∗
Andr´as Gy´arf´as, Mikl´os Ruszink´o
Computer and Automation ... vertices can be partitioned into three monochromatic cycles. From this, using
our earlier results, actually it follows that we can partition all the ver tices into at
most...
Báo cáo toán học: "A note on graphs without short even cycles" pptx
... led to this work.
References
[1] N. Alon, S. Hoory, N. Linial, The Moore bound for irregular graphs, Graphs and
Combinatorics 18 (2002), 53–57.
[2] N. Biggs, Algebraic Graph Theory, Cambridge University ... series of dense graphs of high
girth, Bull. Amer. Math. Soc. 32 (1995), 73–79.
[9] F. Lazebnik, V. A. Ustimenko and A. J. Woldar, Properties of Certain Families of
2k–Cycle Free Grap...
Báo cáo toán học: "Partitioning 3-edge-colored complete equi-bipartite graphs by monochromatic trees under a color degree condition" doc
... Partitioning complete multipartite graphs by
monochromatic trees, J. Graph Theory 48 (2005), 133-141.
[6] M. Kano and X. Li, Monochromatic and heterochromatic subgraphs in edge-colored
graphs - a ... Partitioning by monochromatic trees, J. Combin.
Theory. Ser. B 68 (1996), 218-222.
[4] Z.M. Jin, M. Kano, X. Li and B. Wei, Partitioning 2-edge-colored complete multipar-
tite grap...
Báo cáo toán học: " On externally complete subsets and common fixed points in partially ordered sets" potx
... point set which is a complete lattice. Moreover, the common fixed point
set
Fix
(
T
)
is a complete lattice.
Proof.Let
T
0
∈
T
be the map for wh ich Fix(T
0
)=X
0
is a nonempty complete lattice.
Since ... we characterize the externally complete subsets of trees.
Theorem 2.1. Let X be a tree. A subset M of X is externally complete if and only if M
is convex, Dedekind complete, and a...
Báo cáo toán học: "ON RAMSEY MINIMAL GRAPHS" doc
... minimal graphs for match-
ings,inThe Theory and Applications of Graphs (G.Chartrand, ed.) Wiley (1981) pp.159–168.
[5] S.A.Burr, P.Erd˝os, R.J.Faudree, C.C.Rousseau and R.H.Schelp, Ramsey minimal graphs ... infinite
number of graphs J such that J → (F, G)butifwedeletefromJ any edge e the graph J − e
obtained in this way does not have this property.
Introduction. All graphs in this no...
Báo cáo toán học: "Symmetry Breaking in Graphs" pptx
... possible orbits and providing 2-distinguishing colorings for
graphs with 6-orbits, and graphs without 6-orbits, but with 3-orbits. Clearly
graphs with largest orbit size 2 can be 2-distinguished. ... an involution and
{e, σ
n
2
} is the center of D
n
.
The non-trivial subgroups of D
n
fall into one of three types: a subgroup
of <σ>, the cyclic half of D
n
, a subgroup isomorph...
Báo cáo toán học: "Ramseyan Properties of Graphs by Ermelinda DeLaVina" doc
... a property P of graphs will be called Ramseyan if large
graphs from P contain large monochromatic subgraphs. It is easy to see that P is
Ramseyan if and only if large enough graphs from P have ... Examples of critical P (r, b) graphs are
disjoint unions of b − 1 copies of of complete k-partite graphs in which every part
has r − 1 vertices. Other critical graphs can be obtained...
Báo cáo toán học: " Orthogonal Colorings of Graphs" ppt
... and planar graphs are 5-
degenerate. Obviously, d-degenerate graphs have a greedy coloring with d +1colors. The
next theorem bounds the k-orthogonal chromatic number of d-degenerate graphs.
Theorem ... the
chromatic number. We also study the structure of graphs having an optimal or perfect
orthogonal coloring, and show that several classes of graphs always have an optimal or
perfect...
Báo cáo toán học: "Nim-Regularity of Graphs" docx
... classes of shriekless
graphs correspond to integer partitions.
Proposition 3.5. Shriekless graphs not containing K
−
5
correspond to integer par-
titions which either have three or fewer parts ... complement of such a graph either has no edges or consists of the the
disjoint union of three or fewer complete graphs.
Proof. The complement of K
−
5
is a graph on five vertices with onl...
Báo cáo toán học: "Online Coloring Known Graphs" docx
... generality, α ≥ n/ log n.Letq =(1/2) log
n/α
n. Before coloring,
randomly partition the n vertices into n/q blocks, each of size q, ignoring the
remainder. Greedily color the vertices of each block ... uncertainty is which x out
of k/2 block-vertices are being presented in each round.
We shall describe three strategies for Alice that force Bob to use many colors.
A strategy involves spe...
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