Decompositions of graphs into cycles with chords

Autor: Richard H. Schelp, Hao Li, Paul Balister

Publikováno v: Journal of Combinatorial Theory, Series B
Journal of Combinatorial Theory, Series B, Elsevier, 2018, 128, pp.47-65. ⟨10.1016/j.jctb.2017.07.002⟩

We show that if G is a graph on at least 3 r + 4 s vertices with minimum degree at least 2 r + 3 s , then G contains r + s vertex disjoint cycles, where each of s of these cycles either contain two chords, or are of order 4 and contain one chord.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b69ebe7c3cf03d4d39eec88eb46bd18e
https://hal.archives-ouvertes.fr/hal-01726045

Coloring vertices and edges of a graph by nonempty subsets of a set

Autor: Richard H. Schelp, Paul Balister, E. Gyri

Publikováno v: European Journal of Combinatorics. 32(4):533-537

A graph G is strongly set colorable if V(G)∪E(G) can be assigned distinct nonempty subsets of a set of order n, where |V(G)|+|E(G)|=2n−1, such that each edge is assigned the symmetric difference of its end vertices. We prove results about strongl

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ef983dd134e67bdfe90e696d3704ed01

Connected graphs without long paths

Autor: Jenö Lehel, E. Gyri, Richard H. Schelp, Paul Balister

Publikováno v: Discrete Mathematics. 308(19):4487-4494

We determine the maximum number of edges in a connected graph with n vertices if it contains no path with k+1 vertices. We also determine the extremal graphs.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::78a423425aba0823b4be47f549c20b85

Adjacent Vertex Distinguishing Edge‐Colorings

Autor: Jenö Lehel, Richard H. Schelp, E. Gyo dblac, Paul Balister

Publikováno v: SIAM Journal on Discrete Mathematics. 21:237-250

An adjacent vertex distinguishing edge-coloring of a simple graph $G$ is a proper edge-coloring of $G$ such that no pair of adjacent vertices meets the same set of colors. The minimum number of colors $\chi^\prime_a(G)$ required to give $G$ an adjace

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::9d66697cbec1ff71369282bffbb382df
https://doi.org/10.1137/s0895480102414107

Mono-multi bipartite Ramsey numbers, designs, and matrices

Autor: Paul Balister, András Gyárfás, Jenö Lehel, Richard H. Schelp

Publikováno v: Journal of Combinatorial Theory, Series A. 113:101-112

Eroh and Oellermann defined BRR(G1, G2) as the smallest N such that any edge coloring of the complete bipartite graph KN, N contains either a monochromatic G1 or a multicolored G2. We restate the problem of determining BRR(K1,λ, Kr,s) in matrix form

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::032cec68774081dab3ed9ea088e74241
https://doi.org/10.1016/j.jcta.2005.07.003