10,584 research outputs found
Odd Wheels in Graphs
AbstractFor k⩾1 the odd wheel of 2k+1 spokes, denoted by W2k+1, is the graph obtained from a cycle of length 2k+1 by adding a new vertex and joining it to all vertices of the cycle. In this paper it is shown that if a graph G of order n with minimum degree greater than 7n/12 is at least 4-chromatic then G contains an odd wheel with at most 5 spokes
Three results on cycle-wheel Ramsey numbers
Given two graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. We consider the case that G1 is a cycle and G2 is a (generalized) wheel. We expand the knowledge on exact values of Ramsey numbers in three directions: large cycles versus wheels of odd order; large wheels versus cycles of even order; and large cycles versus generalized odd wheels
Families of Graphs With Chromatic Zeros Lying on Circles
We define an infinite set of families of graphs, which we call -wheels and
denote , that generalize the wheel () and biwheel ()
graphs. The chromatic polynomial for is calculated, and
remarkably simple properties of the chromatic zeros are found: (i) the real
zeros occur at for even and for odd;
and (ii) the complex zeros all lie, equally spaced, on the unit circle
in the complex plane. In the limit, the zeros
on this circle merge to form a boundary curve separating two regions where the
limiting function is analytic, viz., the exterior and
interior of the above circle. Connections with statistical mechanics are noted.Comment: 8 pages, Late
Testing 4-critical plane and projective plane multiwheels using Mathematica
In this article we explore 4-critical graphs using Mathematica. We generate graph patterns according [1, D. Zeps. On building 4-critical plane
and projective plane multiwheels from odd wheels, arXiv:1202.4862v1]. Using the base graph, minimal planar multiwheel and in the same time minimal according projective pattern built multiwheel, we build minimal multiwheels according [1], Weforward two conjectures according graphs augmented according considered patterns and their 4-criticallity, and argue them to be proved here if the paradigmatic examples of this article are accepted to be parts of proofs
Cohomologie de Chevalley des graphes ascendants
The space of all tensor fields on ,
equipped with the Schouten bracket is a Lie algebra. The subspace of ascending
tensors is a Lie subalgebra of . In this paper, we
compute the cohomology of the adjoint representations of this algebra (in
itself and ), when we restrict ourselves to cochains
defined by aerial Kontsevitch's graphs like in our previous work (Pacific J of
Math, vol 229, no 2, (2007) 257-292). As in the vectorial graphs case, the
cohomology is freely generated by all the products of odd wheels
On building 4-critical plane and projective plane multiwheels from odd wheels
We build unbounded classes of plane and projective plane multiwheels that are
4-critical that are received summing odd wheels as edge sums modulo two. These
classes can be considered as ascending from single common graph that can be
received as edge sum modulo two of the octahedron graph O and the minimal wheel
W3. All graphs of these classes belong to 2n-2-edges-class of graphs, among
which are those that quadrangulate projective plane, i.e., graphs from
Gr\"otzsch class, received applying Mycielski's Construction to odd cycle.Comment: 10 page
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