Showing papers in "Journal of Combinatorial Theory, Series B in 2009"

TL;DR: In this paper, a relation between the signed Bollobas-Riordan polynomials of dual graphs has been established for graphs embedded into a surface to a duality with respect to a subset of edges.

TL;DR: It is proved that every graph of tree width at least k has a bramble of order @W(k^1^/^2/log^2k) and size polynomial in n and k, and that for every k there is a graph G of treewidth @W (k) such that every brambles of G of order k^1/^1+^2^+^@e has size exponential in n.

TL;DR: This paper describes the determination of all orientably-regular maps and hypermaps of genus 2 to 101, and all non-orientable regular maps andhyper maps of genus 3 to 202, and extends the lists obtained by Conder and Dobcsanyi (2001) of all such maps of Euler characteristic -1 to -28.

TL;DR: A best upper bound is found on the third largest eigenvalue that is sufficient to guarantee that G has a perfect matching when n is even, and a matching of order n-1 whenn is odd.

TL;DR: It is shown that, for every l, if a graph contains no odd K"l-expansion then its chromatic number is O(llogl), and that given a graph and a subset S of its vertex set, either there are k vertex-disjoint odd paths with endpoints in S, or there is a set X of at most 2k-2 vertices such that every odd path with both ends in S contains a vertex in X.

TL;DR: The minimum number of moves needed for Maker in order to win unbiased Maker-Breaker games played on the edge set of the complete graph K"n on n vertices is estimated.

TL;DR: It is shown that, if G has a vital linkage with p components, then G has tree-width bounded above by a function of p, which is the major step in the proof of the unproved lemma from Graph Minors XIII.

TL;DR: It is proved that for any s and k, there exists a constant N=N(s,k,a) such that every 312(a+1)-connected graph with at least N vertices either contains a subdivision of K"a","s"k or a minor isomorphic to s disjoint copies of K"-a","k.

TL;DR: It is proved that there exists n"1 such that for every even n>=n"1, R(C"n,C" n, C"n)=2n.

TL;DR: It is shown that there is an infinite set N of primes congruent to 1(mod16) such that OP(F) has a solution for any 2-regular graph F of order n@?N.

TL;DR: The existence of simplicial extremes shows that (even-hole, diamond)-free graphs are @b-perfect, which implies a polynomial time coloring algorithm, by coloring greedily on a particular, easily constructable, ordering of vertices.

TL;DR: It is proved that every planar graph without 5- and 7-cycles and without adjacent triangles is 3-colorable.

TL;DR: It is proved that, if M does not contain all simple rank-2 matroids, then h(k) is finite and is either linear, quadratic, or exponential.

TL;DR: It is proved that every planar graph has an edge partition into three forests, one having maximum degree at most 4.

TL;DR: The spectra of cubic plane graphs whose faces have sizes 3 and 6 are determined and a conjecture of Fowler is proved, which asserts that all their eigenvalues come in pairs of the form {@l,-@l} except for the four eigen values {3,1,1,-1, 1}.

TL;DR: It is shown that with the exception of the Heawoodgraph, the Moebius-Kantor graph, the Pappus graph, and the Desargues graph, a cubic symmetric graph X of girth 6 is a normal Cayley graph of a generalized dihedral group.

TL;DR: It is shown that f"A uniquely determines A, up to permuting rows and (simultaneously) columns, and similarly for real A.

TL;DR: It is proved that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the numberof vertices of the graph.

TL;DR: In this article, it was shown that any oriented graph G on n vertices with minimum indegree and outdegree at least (1/2-o(1))n contains a packing of cyclic triangles covering all but at most 3 vertices.

TL;DR: It is proved that there is a tree-decomposition of a matroid that ''displays'' all of the maximal tangles, and when M is representable over a finite field, each tangle of sufficiently large order ''dominates'' a large grid-minor.

TL;DR: Some new bounds for the clique and independence numbers of a graph in terms of its eigenvalues are given and it is shown that this inequality is tight up to factor of 4 for almost all d-regular graphs.

TL;DR: A conjecture on equitable r-colorings of graphs with maximum Ore-degree at most 2r, which extends the Chen-Lih-Wu Conjecture and one of one of the earlier conjectures is proved.

TL;DR: It is shown that the degree sequences of all even factors in a digraph form a jump system if and only if the digraph is odd-cycle-symmetric, and it is suggested that even factors are a natural generalization of matchings.

TL;DR: It is proved that, given integers l,q>=2 and n there exists an integer @a such that, if M is a simple matroid with no l+2 point line minor and at least @aq^r^(^M^) elements, then M contains a PG(n-1,q^')-minor, for some prime-power q^'>q.

TL;DR: The chromatic polynomial P"G(q) of a loopless graph G is known to be non-zero (with explicitly known sign) on the intervals (-~,0), (0,1) and (1,32/27) as discussed by the authors.

TL;DR: It is shown that for any infinite field K and any K-representable matroid N there is an excluded minor for K- representationability that has N as a minor.

TL;DR: This paper answers the following judicious partition question of Bollobas and Scott in the affirmative: for any positive integer k and for any graph G of size m, does there exist a partition of V(G) into V"1,...,V"k such that the total number of edges joining different V"i is at least k-1km?

TL;DR: A theory of nonmetric tight spans provides a unified duality framework to the weighted maximum multiflow problems, and gives a unified interpretation of combinatorial dual solutions of several known min-max theorems in the multiflow theory.

TL;DR: It is proved that for each k and n there exists a constant c such that, if M is a matroid with rank at least c, then either M has k disjoint cocircuits or M contains a U"n","2"n-, M(K"n)-, or B(K'n)-minor.

TL;DR: The regular t-balanced Cayley maps on semi-dihedral groups for any t are classified and, for every positive integer m, 4m-valent regular (2m+1)-balanced Cayleys on Semi-Dihedral groups are constructed.