TY - GEN

T1 - The maximum k-differential coloring problem

AU - Bekos, Michael A.

AU - Kaufmann, Michael

AU - Kobourov, Stephen

AU - Veeramoni, Sankar

PY - 2015

Y1 - 2015

N2 - Given an n-vertex graph G and two positive integers d, k ∈ N, the (d, kn)-differential coloring problem asks for a coloring of the vertices of G (if one exists) with distinct numbers from 1 to kn (treated as colors), such that the minimum difference between the two colors of any adjacent vertices is at least d. While it was known that the problem of determining whether a general graph is (2, n)-differential colorable is NP-complete, our main contribution is a complete characterization of bipartite, planar and outerplanar graphs that admit (2, n)-differential colorings. For practical reasons, we also consider color ranges larger than n, i.e., k > 1. We show that it is NP-complete to determine whether a graph admits a (3, 2n)-differential coloring. The same negative result holds for the (⌊2n/3⌋, 2n)-differential coloring problem, even in the case where the input graph is planar.

AB - Given an n-vertex graph G and two positive integers d, k ∈ N, the (d, kn)-differential coloring problem asks for a coloring of the vertices of G (if one exists) with distinct numbers from 1 to kn (treated as colors), such that the minimum difference between the two colors of any adjacent vertices is at least d. While it was known that the problem of determining whether a general graph is (2, n)-differential colorable is NP-complete, our main contribution is a complete characterization of bipartite, planar and outerplanar graphs that admit (2, n)-differential colorings. For practical reasons, we also consider color ranges larger than n, i.e., k > 1. We show that it is NP-complete to determine whether a graph admits a (3, 2n)-differential coloring. The same negative result holds for the (⌊2n/3⌋, 2n)-differential coloring problem, even in the case where the input graph is planar.

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U2 - 10.1007/978-3-662-46078-8_10

DO - 10.1007/978-3-662-46078-8_10

M3 - Conference contribution

AN - SCOPUS:84922051449

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 115

EP - 127

BT - SOFSEM 2015

A2 - Italiano, Giuseppe F.

A2 - Margaria-Steffen, Tiziana

A2 - Pokorný, Jaroslav

A2 - Quisquater, Jean-Jacques

A2 - Wattenhofer, Roger

PB - Springer-Verlag

T2 - 41st International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2015

Y2 - 24 January 2015 through 29 January 2015

ER -